First Card Bonus Clarification

Actually had to test some parts of this myself to be sure. First off, from what I saw, the first card bonus does affect the first card, along with the extra attack. I dealt approximately 3000 damage with an Arts card in the first slot, and then 6000 with the same servant using a Buster card first, on an identical enemy. I also noticed that the damage from the extra attack went up significantly when a Buster was used to start compared to a Arts card.

From my own experience, I rarely use an Arts first if I only have one. In terms of net gain of NP gauge, it might be the same, but when it's spread like that (assuming you're at the first draw and using multiple servant's in the turn), you had a servant use what might be their only arts card, and only gained 8 or so on their gauge. There's also the fact that the other two first slot bonuses are typically more immediate, and can have a snowballing effect, either making crits next turn, or eliminating an enemy to reduce the damage you take, along with overkill bonuses. Putting an Arts card first splits it's maximum NP gain among all of the cards instead.

When you start seeing how it affects individual servants, this can change, as their own NP charge rates can lead to greater gains or help make up for a servant's own horrible NP gain, but on paper, it doesn't add anything.

All first card bonus apply to all cards, First and Extra included.

One thing to remember is that generation works per hit in attack animation. Some Servants have very meh Arts card but amazing Quick or Buster cards (Like Jack and Okita with 2-hit Arts and 5-hit Quick), and you will generate more NP from them with leading Arts than from that Arts in third position.

Side note: this site needs to list hitcount on cards somewhere.