Believe it or not a good source of those is the Bible. Every language knows what do with them, either pronounce natively or a direct analogue; Ivan/John and so on.
This depends on your concept of how names work. Some people (often dependent on native language of those people) think names should be translated, but to me they're more like a token than other words.
If your name is Xinyi, your name in English is Xinyi, some people would disagree and say your name in English is Joy; whilst xinyi means joy (IIRC) that's not how names [should] work [IMO].
This might relate in part to how we use a lot of foreign language words for names in UK English. Like how Charis (biblical Greek) is a different name to Grace (modern English) but d both derive from the same meaning.
Yes, for sure, in the end you should call people what they want to be called. I know lots of Chinese people who chose an English name rather than put up with hearing their Chinese name horribly mangled all the time, and I know other Chinese people who prefer to go by their Chinese name and coach people how to say it properly. Or as close as we can get.
In my case sometimes people have trouble with 'Sean' (Irish for John), so I just tell them to say whatever style of John they're most comfortable with. Since it's a biblical name they'll have heard John before in their own language and have access to something familiar.