Hi!

1) What does в мерцании светил mean? And where are the accents?
=> в мерцАнии светИл
=> Here "светила" is the equivalent of "звёзды". If you look at the stars they seem to be twinkling (an optical illusion). Мерцание = twinkling.

2) Why чтоб (Не потому, чтоб я Её любил) and not что as in other cases?
=> чтоб = что+бы = что
=> I don't think it's a very specific case, it's probably just an outdated style more appropriate in poetry than in the normal speech. I think if you'd use "что" here it would be just as fine as "чтоб".

3) What does томлюсь mean? And what is its infinitive form?
=> томиться
=> Literary, "томиться" means "being slow cooked".
=> here it means "bored". Томлюсь с другими = I get bored with the others.
=> However, it can also mean "yearn for someone". For example (33b.ru

Я ею томлюсь-
Хоть уже непредвзято

=> The key to distinguish between those cases (bored and yearn) is the usage of "with" = "с". Think about you're being slowly cooked with someone (=in a presence of someone) or being slowly cooked by [the virtue of wishing to be with] someone (=in a lack of someone).

4) What does И если мне сомненье тяжело mean? Is it сомненье or сомнение?
=> Yes, сомненье = сомнение. A bit outdated form, very appropriate in poetry.

5) What is the infinitive form of ищу? And what does it mean?
=> It's "искать" = "look for something"

6) What does от Неё светло mean?
=> It means "she is a source of light".

Не потому, что от Неё светло, => It's not because she's shiny,
А потому, что с Ней не надо света. => But because I don't need to shine myself (= I can just be myself) when I'm with her.

Hope it helps.