Why are there only 10 playable champions?

There are always ten free champions available so you can try them out before unlocking them. At lower level, it's a standard set, at higher levels, the free champions change every week. You can unlock champions permanently by spending IP you earn every time you play, or RP if you're willing to spend money.

OP either got hit really hard in the head recently or bought himself a LoL account.

Why not?