Both the first option are the proper choice.

Q1 When there is a "了" behind the verb, it usually means the action has been done. However, in this case, "现在" means 'at the moment', so the first is strange if you add '了'. The second is correct, but I would use ‘你发烧了吗' to ask someone if he has done something or is in some situation. Q2 "我没发烧" is more natural.

口语：你现在发烧了吗？ 我没发烧。

现在你发烧吗？我没发烧.Always we say so .

The first one later is correct,and second one correct is former.