Welcome to Hinduism.SE! I will answer from a perspective that will hopefully be understandable to someone coming from one of the Abrahamic faiths—though I will admit, I'm more fluent in Judaism and Christianity than Islam. To speak to your last question first, I once heard it said that the illusion of the Universe exists because "God forgot to laugh." This is of course not literal, but gets at the metaphysical idea.
With regards to your first question, God doesn't make people suffer, people make ourselves the way we are. There is a saying, "God does not punish us for sinning, we punish ourselves by sinning." The original Hebrew word for sin comes from an archery term. It means, "to miss the mark." If you shoot an arrow and miss, do not admonish yourself and quit. Instead keep practicing until you get it right every time.
We should do the same in life—after the initial moment of guilt or sorrow or anger or any other negative ego response we should try again until we get it right every time. This is what it means to be righteous. The shortest distance is a straight line, but we humans like to meander (sin). This isn't terrible so long as we remember to look up and find the path again—the sooner, the better. This is correcting sin.
Airplanes are constantly flying off course because of prevailing winds and turbulence, etc, but the autopilot is constantly looking at where it is and where it needs to be so that it can correct its course. We humans need to do the same, look to a perfect model, God, which is where we need to be, but also look at where we are now. Only then can we course correct.
The reason suffering and sin prevail is because it is easy to forget who "the I" really is. The true I, the knower/observer "inside" has done nothing.
13:12 I will tell you of the wisdom that leads to immortality: the beginningless Bráhman, which can be called neither being nor non-being.
13 It dwells in all, in every hand and foot and head, in every mouth and eye and ear in the universe.
14 Without senses itself, it shines through the functioning of the senses. Completely independent, it supports all things. Beyond the guṇas (qualities), it enjoys their play.
15 It is both near and far, both within and without every creature; it moves and is unmoving. 16 In its subtlety it is beyond comprehension. It is indivisible, yet appears divided in separate creatures. Know it to be the creator, the preserver, and the destroyer.
17 Dwelling in every heart, it is beyond darkness. It is called the light of light, the object and goal of knowledge, and knowledge itself.
18 I have revealed to you the nature of the field (the body & mind; that which seems to be the real you; see "Prakriti" below) and the meaning and object of true knowledge. Those who are devoted to me, knowing these things, are united with me
—Bhagavad Gītā 13:12-18, parenthesis added for topics explained outside the quote
Puruṣa and prakṛiti together are Bráhman.
Purusha is that which is unchanging and is uncaused. The animating causes, fields and principles of nature is Purusha in Hindu philosophy. Hinduism refers to Purusha as the soul of the Universe, the universal spirit present everywhere in everything and everyone all the times. Purusha is the Universal Principle that is eternal, indestructible, without form, and all-pervasive. It is Purusha in the form of nature’s laws and principles that operate in the background to regulate, guide and direct change, evolution, cause and effect. It is Purusha, in Hindu concept of existence, that breathes life into matter, is the source of all consciousness, one that creates oneness in all life forms, in all of humanity, and the essence of Self. It is Purusha, according to Hinduism, why the universe operates, is dynamic and evolves, as against being static.
—Wikipedia, "Purusha", English ed.
And it is contrasted with Prakṛiti. "Material reality, or Prakrti, is everything that has changed, can change and is subject to cause and effect." (Ibid.) Prakṛiti is "the material world, nature, matter, physical and psychological character, constitution, temper, disposition." (Wikipedia, "Prakṛti", English ed.)
Prakriti is the potency that brings about evolution and change in the empirical universe. It is described in Bhagavad Gita as the "primal motive force". It is the essential constituent of the universe and is at the basis of all the activity of the creation.
Prakriti is closely associated with the concept of Maya (illusion).
This gets to the heart of your question. The body & thoughts we believe ourselves to be (also "the field" in the above Bhagavad Gītā quote) is Prakṛiti. "The I" that you know yourself to be is Puruṣa. As described above, Prakṛiti is changeable and Puruṣa is not. Prakṛiti has causes, Puruṣa has no cause. Thus, "the I" is not affected by kárma (action). Everything we experience which is not "the I" itself, is "the I" masked by the illusion of māyā́.
This answer is quite lengthy, so I'll not answer the last question but to say that this reality is all līlā. Nothing that seems painful here, to us, is real or can harm God. It's a dance, a theatrical play in which God is all of the actors as well as the audience, it is a game through which God can know about himself and amuse himself. But, for a more complete answer, see here.