What are the 16 qualities of Sri Rama? Are all of them humanly possible to achieve?
Was Rama born with those qualities or is there any evidence of him striving to acquire those qualities and get better at them through practice?
As far as I understood, Sri Rama was not an incarnation of Vishnu, as commonly believed.
I think you are referring to Bala Kanda 1st Sarga, wherein Sage Valmiki asks Sage Narada to tell about a person, who possess the qualities
गुणवान् (guṇavān = principled person)
वीर्यवान् (vīryavān = potential one)
धर्मज्ञः (dharmajñaḥ = conscientious)
कृतज्ञः (kṛtajñaḥ = redeemer)
सत्य वाक्यो (satya vākyo = truth-teller)
धृढ व्रतः (dhṛḍha vrataḥ = self-determined in his deed)
चारित्रेण च को युक्तः (cāritreṇa ca ko yuktaḥ = blent with good-conduct)
सर्व भूतेषु को हितः (sarva bhūteṣu ko hitaḥ = benign, in respect of all beings)
विद्वान् (vidvān = adept)
समर्थः (samarthaḥ = ablest)
एक प्रिय दर्शनः (eka priya darśanaḥ = uniquely good-looking)
आत्मवान् (ātmavān = courageous)
जित क्रोधो (jita krodho = one who has controlled his anger)
द्युतिमान् (dyutimān = brilliant one)
अनसूयकः (anasūyakaḥ = not jealous)
बिभ्यति देवाः च जात रोषस्य संयुगे. (kasya bibhyati devāḥ ca jāta roṣasya saṃyuge = even whom do the gods fear, when provoked to war)
If you are asking about these qualities, then the answer lies in Sage Narada's reply itself.
The person, who posses all the above qualities is one and only SRI RAMA.
Sri Rama possessed some qualities by birth and after acquiring mastery over wielding of various weapons, he became invincible.
A couple of commentaries on Valmiki Ramayana I found at this link cover Sri Rama's qualities in good detail.
Valmiki’s Query to Narada 1.1.2
Valmiki asks: who among men is the greatest? Who is the person embellished with all virtues? Who is guṇavān, or who has good qualities like happiness, benevolence, etc.? Who is vīryavān or one with special power that comes from possessing divine weapons and strength? Who is dharmajña, or one well-versed in the Vedic and Smrti literature and knows the niceties of religion, philosophy and morality? Who is kṛtajña or one who forgets evil deeds of others and considers even one good deed with much gratefulness? Satyavākya is one who speaks whatever he sees or hears. Drdhavrata, is one, even though surrounded by adversities, never forsakes the special vow to uphold dharma.
Rama’s Virtues 1.1.3-6
Rama possesses character and wealth [cāritreṇa], looks after the welfare of all in this world [sarva-bhūteṣu-hitaḥ] as well as the next. He wishes Ravana, his greatest enemy well and wishes him heaven after death. He knows all about atman, anatman, etc. has the skill of social behaviour and of ruling the subjects and is therefore known as samartha, is attractive, always remains beautiful and whose body is uniformly good-looking [eka priya darśanaḥ]. Another view is that Rama is a person who is good-looking to only one individual. But what purpose does this interpretation serve?
Rama is ātmavān that is one who has control over his desires and senses and has conquered his mind. He is described as jitakrodha. Krodha includes desire to kill. But a person who does not indulge in unnecessary or unprovoked violence can be said to have conquered anger. He has that special glow emanating from a beautiful body which compels everyone to keep on looking, and it is known as dyuti (glow) and one who possesses that special grace is dyutimān. Anasuyaka is one who is not jealous of another’s knowledge, wealth or progress. Jealousy is asuya and one who is not jealous is known as anasūyaka. “Who is such a divine person who possesses all these qualities? I want to hear of him”. That was the query of Valmiki. It is quite unusual to find these qualities together in one place. Therefore I have very great anxiety to know it. I ask you because you alone are able to answer”. The word maharsi is an adjective. It is used purposefully to denote that Narada has the power to go beyond the senses. He is trilokajnah or the knower of the three worlds, bhuh, bhuvah and svah. Narada knows whatever has happened or is happening in them.
Valmiki’s query 1.1.2-6
Valmiki cites various qualities and asks Narada as to who in this world is endowed with all virtues?
Here the word guna means special excellences, which are separate from the ordinary visible qualities, because the reply to this question mentions such excellences.
The excellence by which one defeats the enemies without himself being injured is called Viryam and one who has it is called Viryavan.
- Dharmajna is a person who knows both the general and special dharmas.
- Krtajna is he who considers even a little help rendered by others as great.
- Satyavak is one who speaks the truth under all circumstances.
- Drdhvrata is he who does not break a vow until it yields the desired result.
- Caritra is the behaviour that has come down as a tradition in one’s family. Caritrena Yuktah is one who possesses all good behaviour.
- The phrase Sarvabhutesu implies that the person does good even to those that offend him.
- Aidvan knows everything worthy of knowing.
- Samartha is a person who is able to perform tasks which others cannot.
- Kascaica priyadarsanah is the person whose sight is endlessly dear to all. Sight can become dear only for handsome limbs. Hence it means a person who has exquisite limbs.
- Atmavan is one who controls his mind or who is courageous.
- Jitakrodhah is a compound word, in this krodha implies all the six bad qualities of the mind, namely kama (lust), krodha (anger), lobha (avarice), moha (infatuation), mada (intoxication or arrogance) and matsarya (envy). Jita is one who has subdued them. So the phrase denotes he who has subdued all the six internal enemies.
- Dyutiman is brilliant.
Asuya is finding flaws even in excellences; he who is free from asuya or feared by gods or demons in battles is anasuyaka.
Etat means he who possesses all the qualities cited above. Trilokajna is a person whose knowledge encompasses all the three worlds. Amantrya implies he attracted Valmiki’s attention for achieving similarity of thought.
Kasya Bibhyati Devasca shows the abundance of qualities that makes gods afraid. This does not apply to Brahma etc. It relates to somebody else (Rama).
Again, since an ordinary mortal cannot be expected to possess all the great qualities cited in Valmiki’s question, it finally culminates in the Supreme God who came down in human form for the world’s protection. Narada is happy for the opportunity he luckily got to analogise the excellencies of the Lord. This is indicated by the word Prahrsta. Buddhva Laksyami means, ‘I am going to describe a great person who has the numerous rare qualities cited by you’. The verb Sruyatam in the imperative mood gives the idea that it was the right time for Valmiki to hear about that great man.