Good questions!

Antwoorden
Q1 ''Wat doet hij in het park'' doesn't necessarily mean he is there *right now*. But you can infer where he is now from sentence 1 and 2 together, or sentence 4.
Q2 In (4), ''lezen'' is a verb. It described the action he is performing .
Q3 In this case it's comparable to the gerund in English ("he is reading"). ''Hij is aan het lezen'' simply is the/one way to form the gerund in Dutch. You are right, instead of saying ''Wat doet hij daar?" you can also say ''Wat is hij daar aan het doen?"
Q4 I'm not sure if I can generalize it (as there may be some situational deviations), but it would *probably* need an article, yes. Though it's a little hard to turn the verb ''lezen'' into a noun in this sentence structure.

Hopefully, this helps you in any way possible.

Wat doet hij in het park

I have some questions about the sentence below

1:A Waar is LiMing naar toe gegaan?

Hij is nog steeds in het park. = He is still in the park.

2:B Hij is naar het park gegaan.
3:A Wat doet hij in het park?
4:B Hij is daar een boek aan het lezen. 

Lezen = reading (verb)
He is reading now. Therefor you write it in the present tense

QUESTIONS
Q1 in (3), How can I get implication that LiMing is still in the park? or I cannot get it ONLY according to the two sentences above.
Q2 in (4) Is the “lezen” a noun or a verb?
Q3 if it is a verb, why "is ... lezen" is used here, to answer a present tense "wat doet"？
Q4 if it is a noun, does it need an article?

Ik weet niet of je hier iets aan hebt. = I don't know if you  have something about it.