1- yeah, you can plug a modded S&S straight into a line level channel on a mixer. Most modded S&S machines have a single mono jack output but theres no reason why you couldn't split the signal into 2 X mono for a stereo mixer input with a Y cable. S&S machines cannot be used as effects units to effect other signals, you can only use the internal sounds.
2- Virtually every modded S&S machine will have a pitch control that not only takes the pitch up and down but does so by making the machine run faster or slower. This means its entirely possible to create a loop with a loop switch and then sync it in time with a record using the pitch controls. It might take a bit of practice but its possible.
3- i think most people use kit like S&S machines live in a more random manner rather than trying to sync things up i.e, bursts of glitching or spot effects. Apparently when Simon Posford from Twisted Records plays a Hallucinogen In Dub set with a circuitbenders Speak&Spell they have a 'Speak&Spell face pulling session'. I'm not entirely sure what that means but it sounds like a laugh