Studying Kanji can easily become one of the most overwhelming challenges of studying Japanese. Even people who speak the language decently have difficulty reading and writing Kanji.
As you have no doubt discovered, learning a single 漢字｛かんじ｝ can be a challenge. Unfortunately, you should do your best to learn everything about the character you can.
While you've only touched on it, stroke order IS important, but the more you practice the easier it gets. You'll start to develop a natural feel for it over time.
But do I really need remember onyomi & kunyomi for each of them?
Yes, you do. I'm sorry to say it, but your example of 人 is a classic example of why you should learn all the readings.
Below are some common words that use 人。
仲人 【なこうど】(matchmaker -- less common, but uses the -と reading)
本人｛ほんにん｝(the person himself)
The best way to learn the readings of a kanji is to see common usages of it. Look up all the words you can that use the character, and learn how it would be read in different situations. Of course, practice, practice, practice. It will take a lot of effort on your part.
If you see the character on its own (hiragana on both sides), you've likely got an kunyomi. This isn't guaranteed, but it is the case more often than not.
If you see the character with other kanji, it's likely a onyomi. This too isn't guaranteed, but it is also the case more often than not.
The fact of the matter is, you have to expose yourself to Japanese writing a lot before you start to develop an intuitive feel for how things could be read. Honestly, I still misread some characters when I go off of intuition, but as I keep saying, practice makes perfect.
How important is is to know the onyomi and kunyomi readings? How is it useful?
Japanese people use both onyomi and kunyomi readings all the time. It's useful to know both of them because otherwise you will never be able to read the language fluently.
Suppose we came across a word with new kanji somewhere, is there a way to know how to read it?
The only way you will know how to read the characters is if you have had prior experience with it. This will require a lot of practice and a lot of patience. Practice makes perfect here, and you will need a lot of practice.
Take comfort in knowing that kanji is hard for Japanese natives and foreigners alike. I have known several Japanese people who struggled with reading kanji. They could read the common, basic characters, but a lot of the time they needed help from someone who had a better knowledge of the characters. I have even been in reading groups where educated people have needed help reading characters, simply because it was outside their area of expertise. It would be the same thing if I started talking about
electrical induction to a doctor. Sure, it's English, but they haven't studied it before, and likely won't fully understand what the term
electrical induction means.