Your questions are all equivalent. They would be more natural with 'suddenly' earlier in the question. I think that you need to do that to emphasise the suddenness. In terms of a more natural way to say it: 'another question just came to mind'. I think that 'came to mind' is idiom - it may not be grammatically correct.

the context is I was asking a question to a friend, and during the discussion, I had another question, so can I say 'another question came to my mind' to him. Or how would say in this case? thanks.

I prefer to know the context before translating your sentence. If a thought or idea ​occurs to you, it comes into ​your ​mind. For the frist sentence, I think using present perfect is incorrect. I also think the word 'suddenly' is redundant​.

1) is present perfect; (2) and (3) are simple past. I think they all mean your 中文句子; however I'd rephrase the 句子 as " 我突然想到一个问题" or "我才想起来" just to be clear that you don't suddenly have a problematic situation instead of having a question to ask.