1. You'll get the Master Sword later on, and can take on a sidequest to get Biggoron's sword after that.
2. Of course, but don't buy a Hylian shield! Go to Kakariko Graveyard, there's a shield under one of the graves (if you can stand up to a ReDead). Finally, you'll get the Mirror Shield very late in the game. I personally prefer to use the Deku Shield with Young Link when not around fire, since you can move when using it.
3. You don't--you'll get arrows and a bow later on.
4.The first bomb bag you can get is in Dodongo's Cavern.