(This is my first post)

I've been trying to play as an archer, but it's almost impossible because:
1. My arrows fall to the ground half the time.
2. sometimes the arrows will miss/not hit the enemy EVEN THOUGH THE CROSSHAIR IS RIGHT ON THEM
3. Sometimes, when equipping my bow, theres a 1-5 second delay before I can use it,
Sometimes it doesn't draw, at all...
5. When sneak attacking from a distance, the arrows will fade out of view.

Is there any way to fix these issues?

Firstly, welcome to the forums.

As for your problems these are all known issues. Hopefully you'll find this useful.

1: I'm going to assume you're fully drawing the bow as needed in which case the arrows should fly. It's a well documented fact that the hit boxes for objects in this game are noticeably larger than the objects themselves, this means if you're in cover your crosshair and even character model may clearly show the bow will five over the wall, but you'll still hit it. Also I've noticed if you try to fire too quickly and press R1 again during firing arrows will simply drop as well.
2: Never had a problem with this myself, if anything I get issues with enemies being hit when I know I missed. Do you get this when there's a distance or height difference between you and your target because while Skyrim doesn't have real life physics arrows do drop during flight, for long distance shots or shots against enemies on high ground you'll need to adjust your aim upwards to compensate for gravity.
3: the PS3 has a unique bug where there is a delay on weapon switching, it's well documented and certainly known to Bethesda, hasn't been fixed though
4: I've read of people having issues of having their bow equipped but being unable to draw but not had it myself. Unequipping and re-equipping via the inventory screen seems to resolve this
5: you're probably noticing the arrow leaving the draw distance. Under-bridge-dwellers from other platforms will tell you this is due to platform hardware limiting the draw distance, one of the guys here tested it with a spell and found that spell projectiles travel much further than arrows without disappearing, if it was a draw distance issue the two projectiles should disappear at the same distance.

I do usually use the report button I was just sick of that certain individual constantly posting nonsense. #2 I do know that sometimes doesn't happen all the time even if you shoot an arrow and it's a direct hit I had my arrow's go through the enemy and land behind them. It's a wierd glitch that doesn't always happen but I've actually had it happen to me on Oblivion as well.