Does the first card effect the extra card when doing brave chains?

Nope. The np isn't affected by the first card bonus, but most of the time should still be played first since a lot have defense down and such debuffs.

From my experience the noble phantasm card is effected by those bonuses. At the very least attack bonuses anyways because I've noticed that with everything else constant NP cards that are played later especially with buster buffs do a bit more damage than otherwise. However in a lot of cases your going to want to play the NP card first. Some examples being if the NP provides defense debuffs, attack buffs just for that turn (like Jack's NP for example), or especially if your making an arts card chain with an arts noble phantasm.