1. Probably something about lighting a candle when you pray, or some similar practice?
2. Google あなご飯 (it's めし, btw). The first one should be for wikipedia. The second and third (at least on my machine) hits relate to the restaurant うえの which appears to be famous for あなご飯. (アナ・ご飯… you know I'll eat most anything but I think I'd have to pass on that one!)
3. "I'll email you again".
4. I think it's just the copula; treat the two parts as two separate clauses.
1. Do you understand what ...にお願いごとをしたり出来ます means? I'm not even sure what type of sentence it is. Is the speaker making a request? And what is ごと likely to refer to?
Edited: Oh, is the writer telling the addressee that the addressee can ask for candles?
3. How do we know that it doesn't mean "You will email me again, won't you"?
1)
お願いごと is one word; "prayer" or "request".
たり is from "~たり、・・・たり". ろうそくにお願い事をする is an example of what you can do in the temple.
This is 願いろうそく in 大聖院, 広島. You can see something written on each candle. They are prayers.
3)
The subject of (では/じゃ)また~するね is ALMOST ALWAYS the writer/speaker. You can consider this is a kind of complimentary close when used at the end of a letter/conversation. Indeed the subject can be the recipient or third person in some specific context, but するよね would be far common even for the case.