Speedrunners are playing the game manually, and sharing the tricks they find for how to exploit game mechanics to speed things up.

There exist something called TAS (tool-assisted speedrun) where you use an emulator with save states and either slow motion or the ability to advance frame-by-frame in order to construct the "ideal" run, but runs constructed these ways generally aren't actually playable by hand because they rely too much on frame-exact timing.

Yes, speedruns are humans playing the game live.

If preprogrammed inputs or whatever are used, the term TAS (tool-assisted speedrun) is used. Calling a TAS a speedrun would be a faux pas.

There’s different varieties of speed running. Some people do it entirely manually, others do Tool Assisted Speedruns (often abbreviated to TAS) where a program provides all the input, allowing frame perfect moves which humans are incapable of. There’s also a slowly growing trend of letting machine learning algorithms loose on games like Mario - that stuff to my knowledge is still at the stage of trying to get an AI to even be able to finish the game at all, but I’m sure with some time and effort we’ll start seeing techniques no one has even thought to try.

Speedrunning is primarily done manually. Some players use fuzzers for discovering tech, but TAS is a separate genre of speedrun and generally more of a novelty than anything.