There are huge texts listing many throws. I break them down into two kinds: sport, and martial. Martial throws are variants of the underlying abstract movement which results is awkward falling for a trained fallee - typically, they get dumped or thrown while a joint is still trapped. Sport throws can still be damaging, but offer the fallee a better possibility of rolling - typically, they are round and large.
Stances and footwork for throwing (and grapping or wrestling) are different from the more upright stances of kick/punch fighting, or sieze/control neutralisation. This is because leverage and balance are primary issues in throwing. A poorly timed throw leaves the thrower open to many serious attacks, but a well timed (responsive) throw is very hard to avoid.
More to follow when I find time...
Takedowns and throws in sparring (and their reversals) can be dangerous to learn - they should be started in slow motion, on mats - and should be only practiced when the "throws and takedowns" rule is announced by the instructor.
Tom Osborn