A) 'I and Simon are going for lunch' is correct. Although, generally, we put others before ourselves so 'Simon and I...' would be 'better'.
B) 'You and I are going
If you know about the terms 'subject' and 'object' in grammar, then 'I' is used for a subject - who is doing the verb; 'me' is used for the object - who is the verb being done to.
If you don't know about that, it might be useful to replace 'I' or 'me' with another similar pronoun. 'I' is similar to 'she', and 'me' is similar to 'her'. So, try using 'she' or 'her' in your sentence and it should be clear for you.
'You and she are going for lunch' vs. 'You and her are going for lunch'
'You and she are going fishing' vs. 'You and her are going fishing'.
So, if 'she' fits, then it is 'I'. If 'her' fits, then it is 'me'.
I also noticed that you are a native speaker. In that case remove the other person/people from the sentence as bhaisahab showed below. 'Me is going for lunch' should sound childlike to a native speaker (children use 'me' before they understand the concept of 'I').
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