1. No, but you'll be wearing things over your face for the majority of the game, I wouldn't worry about it.
2. Yes, but some of the later weapons have better stat-scaling. There are plenty of the materials needed for leveling up weapons to +9, so be sure to try out later ones as you go along (Ludwig's Holy Blade is a thing of beauty). There is only 1 of the final upgrade material in the main game (you can get more from harder chalice dungeons but it's exceptionally rare), so I would save the +10 for when you're sure you have found your weapon of choice.
But yes, if you really wanted to you could use it all the way, but you'd be missing out if you didn't try other things as you got them.
3. Up on the D-Pad will take a chunk of life in exchange for 5 "blood" bullets.