Aagami Karma is actions we do in this birth. This is generally said to be free will. See this question: Is our destiny predetermined? If yes, then why do our actions affect our karma?.
Does Shiva or Vishnu or a Trikalagnani Yogi (who can know past, present, and future) know our Aagami Karma? Or do they just know consequences of our Prarabda Karma?
Yes, Brahman definitely knows what choices we're going to make, because Brahman is the one that causes us to make those choices. But then how is it fair that we are punished for choices that Brahman caused us to make? It's because the choices that Brahman causes us to make now are based on the choices we made in a past birth, and the choices Brahman caused us to make in a past birth are based on our choices in a birth before that, etc., going infinitely far back in time. Here' what Adi Shankaracharya says in his commentary on the Brahma Sutras.
[F]or although the activity of the soul is not independent, yet the soul does act. The Lord indeed causes it to act, but it acts itself. Moreover, the Lord in causing it to act now has regard to its former efforts, and he caused it to act in a former existence, having regard to its efforts previous to that existence; a regressus against which, considering the eternity of the samsâra, no objections can be raised.
Other commentators on the Brahma Sutras say the same thing, as I discuss here. So even though Brahman is the efficient cause of our choices, our choices are still ultimately in our hands.
Yes, the Lord surely knows our Aagami karma.
This universe, which is the grossest of the gross entities, is the form of the Lord. In this Cosmic Form all the past, the present and the future subsist. Permeating this universal cosmic form, with its seven sheaths - consisting of five elements, egoism, and the universal intelligence - there is the Viratpurusha - the Cosmic Divinity. He is the real object of concentration.
Srimad Bhagavata Purana II.1.24-25
So does a jiva have free will?
Vaidyanath: "Sir, I have a doubt. People speak of free will. They say that a man can do either good or evil according to his will. Is it true? Are we really free to do whatever we like?"
Master [Sri Ramakrishna]: "Everything depends on the will of God. The world is His play. He has created all these different things - great and small, strong and weak, good and bad, virtuous and vicious. This is all His maya. His sport. You must have observed that all the trees in a garden are not of the same kind.
"As long as a man has not realized God, he thinks he is free. It is God Himself who keeps this error in man. Otherwise sin would have multiplied. Man would not have been afraid of sin, and there would have been no punishment for it.
"But do you know the attitude of one who has realized God? He feels: 'I am the machine, and Thou, O Lord, art the Operator. I am the house and Thou art the Indweller. I am the chariot and Thou art the Driver. I move as thou movest me; I speak as Thou makest me speak.'"
The Gospel of Sri Ramakrishna, April 15, 1883
Sri Ramakrishna: "People who have realized God are aware that free will is a mere appearance. In reality man is the machine and God is the Operator, man is the carriage and God its Driver."
The Gospel of Sri Ramakrishna, January 5, 1884
The Younger Naren: "Sir, have we any free will?"
Sri Ramakrishna: "Just try to find out who this 'I' is? While you are searching for 'I', 'He' comes out. 'I am the machine and He is the Operator.' You have heard of a mechanical toy that goes into a store with a letter in its hand. You are like that toy. God alone is the Doer. Do your duties in the world as if you were the doer, but knowing all that time that God alone is the Doer and you are the instrument."
The Gospel of Sri Ramakrishna, July 14, 1885
Disclaimer: I mostly agree with @PradipGangopadhyay's answer (upvoted) except the statement that Lord knows our Agami Karma. Please refer all those scriptures before reading this answer.
Agami Karma or any event is NOT "known" by ANYONE. Even though all are predetermined.
Above statement is contradictory, which is explained in 'Free Will' segment.
There is a sharp difference between "knowing" and "believing". Weather forecasting dept. Believes that the X day will have rains but they don't Know it. "Knowing" comes only when something happens; until then, it's just "Believing". Few decades back using various maths, the humans "believed" the earth to be a round. They "knew" only after the satellite photos.
"Know" relates to past, while "Believe" is futuristic. For eternal truths (e.g 1+1), both merges to present.
Let's first start with manifested supreme nature of God (call Vishnu).
Here is how it's impossible to 'know' future by Vishnu:
--------×------------(×, 9/11 attack)---
.......T1...............T2 Event
In above time line, let's assume TrikAl GyAni knows on some ordinary day of 20th century that WTC attack shall happen. His/her states of "knowledge" are T1 and T2 respectively.
Above is a bit complicated logic, hence needs perseverance of mind a bit & you get this infinite recursion, which is impossible. Now this is literally "infinite" and not "too big to be finite". Former is theoretical and latter is practical. Above is just an example of 2 time moments. Think about altogether.
Above proves that with whatever might one has, it's quite impossible for any manifested entity (be it God) to assure future, as it requires infinite resources. But surely it can be predicted to near true accuracy. But that is just prediction, as good as yours or mine. May be ours are less probable to happen.
From scriptures; Krishna 'kind of predicted' following:
BG 11.34 — Droṇa, Bhīṣma, Jayadratha, Karṇa and the other great warriors have already been destroyed by Me. Therefore, kill them and do not be disturbed. Simply fight, and you will vanquish your enemies in battle.
He also added to enjoy the glory of earth after winning the war. Most of his words were true, except Drona. Arjuna was not even a far away reason for Drona's death. No one could kill him. He left his body using KriyA yoga (after forfeiting his only attachment towards AshwatthAmA) at last. One may refer this chapter of Drona Parva, which describes Drona receiving Moksha before his dead body was decapitated by Drishtadyumna.
There is another instance, where after receiving curse from GAndhAri, Krishna let it happen instead of changing it. Here are the words of DwaipAyana:
Vyasa said, ‘The mighty car-warriors of the Vrishni and the Andhaka races have all been consumed by the Brahmana’s curse. O chief of Kuru’s race, it behoveth thee not to grieve for their destruction. That which has happened had been ordained. It was the destiny of those high-souled warriors. Krishna suffered it to take place although he was fully competent to baffle it. Govinda was able to alter the very course of the universe with all its mobile and immobile creatures.
VyAsa as TrikAla GyAni said that Krishna can change the future events. How can one "know" something which is alterable? It shows that the futuristic events can be just believed to be happening with high probability, but can't be known by Any manifestation!
One may ask, what about unmanifested eternal nature of God (call Shiva or Brahman), can it "know"?
Yes, it 'can' know, but it 'doesn't'; even though all creation is manifested from it! Because Brahman is "uninterested" in its creations to remain *NishkAm" and unbound by Karma.
BG 9.8, 9.9 — The whole cosmic order under Me automatically manifests again and again and annihilated at the end.
— O Dhanañjaya, all these Karma cannot bind Me, as I am ever uninterested (and) detached from all these Karma.
For Brahman, all is Bhuta, as Krishna refers in Gita. Which means everything has happened; be it past or future. If we can "know" past, Brahman can "know" (what we call) future too.
However here is the catch: we know only the interesting part of past, not all billions of moments.
For Brahman, nothing is interesting! Hence unknown.
Brahman's actual unmanifested form is eternal and constant. Like how a computer algorithm in absence of external variables would generate always same random number, Brahman as only source & destination, also does the same. It keeps creating/destroying same universe all the time. Here universe means all the past & future events which we live as present and all thoughts we ever generate.
BG 2.12 — Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.
(Just think, why should Krishna say such words when there is something called Moksha!)
If by any chance Brahman is creating different universes every time, then due to infinite regression, we can't ever reach current moment. But that's not the case. Hence it has to be frequency; i.e. universe should repeat itself on every day of Brahma.
Then what changes between 2 universes?
May be nothing or may be which part of universe is experienced by consciousness or may be the type of consciousness. All are beliefs. What we may know is that everything has to be cyclic, if not on Brahma's day then month or year or millennium... It must repeat.
Isn't it contradicting that, even though the Bhuta created by Brahman is predetermined, yet unknown!
Yes, this is called "free will". Because no one Knows what's going to happen, we feel our Will to be free. But in reality it is not. Our Will is generated and terminated by God which roots to One. One variable (as good as constant) can contain only One value!
All above is what I "believe", but don't "know" yet. :-)
I take Shiva and Vishnu as the same God and there can not be two Gods.
yes,Bhagavan of course knows.The definition of Bhagavan is:
utpattim cha vinaasham cha bhutanaam agatim gatim/vetti vidyaam avidyaam cha sa prokto bhagavaan iti.
So God knows the origin, the death, the manners of going and non-going, and about knowledge and ignorance of ALL.
Another definition of God also mentions that God has six qualities termed as Bhaga in entirety.One of these is knowledge.So He must be knowing the present and future activities of each being perfectly.
So theoretically He must be knowing everything,How it is practically possible is beyond our logic and perception, as we are immersed in Maya and God is controller of and unaffected by Maya.
The Trikala-darshi can know only that part which He or She wants to know.But none can become omniscient as none can become God or Bhagavan according to any recognised sect. Brahman is a different concept altogether.
