Not necessarily offended, but how I perceive a prayer depends on the expressed intentions behind it. If they genuinely wish me well, of course not. If they say, "I'll pray for you" in a condescending or hateful way because I don't share their views, I don't feel offended so much as simply alienated from them due to their narrow-mindedness.
On the other hand, some theists have told me that they wanted to pray for me because they really don't want me to end up in Hell. I know they care about me, and of course that makes sense to me in the context of their beliefs. What I think of the belief itself doesn't change that these are people who are wishing the best for me from their perspective. I know what it's like to care about someone and not want them to go to Hell, since I used to hold that belief too.
No.
That depends on what it is about, as I said above. I appreciate expressions of goodwill and concern, so a prayer motivated by such sentiments would "affect" me by engendering positive feelings.
No.
Same. I generally don't see it any differently than I do wishes, whether good or ill, that someone may have for me, even if they don't express them as prayers.