When I stand in between 2 explosions on my sides, very often I get hit by either of them, even though I stand between those two blocks and neither should hit me. Happens all the time, I've been standing there for a while so its not typical "you lagged, you were still standing in the block where explosion took place.

Yes its a bug that knight takes up 2 blocks and can be hit by explosion in either of those. And no, its not lag-related.
There is a lag-related problem when knight gets hit by explosion 2-5 tiles away from current position, by being hit in a place they left ages ago - THAT is a lag problem. Another lag problem is when a knight is teleported backwards and put in between bombs after leaving the place (knight gets stuck trying to move, and when you stop trying to move you get teleported in between 2 bombs like 3-5 blocks away, as if you never left that spot).

Knight should only take up ONE block at a time, unless knight is standing in the middle space between 2 blocks (not 1 pixel away from center of a block, but very close to the middle between 2 blocks).

Best solution would be to tie knights down to blocks and move one block at a time, or auto-center when moving in a different direction, for example: when you move up, your left/right position in the block is centered automatically. That is, if you don't try to move up and left at the same time. IMO, diagonal moves should not be allowed in Bomberman PvP.