as far as chopping for drums, you basically just hear a break, and chop the sounds individually, don't worry about measures/time with them. like take the initial impact as the start of the chop and end it before the next drum, so you have all the air and tail end from it.
but yea its not really about knowing to do it, as much as just wanting to. you never have to chop a drum break there are enough drumsounds out there, but in them old songs, specifically between like 67 and 73 the way music was recorded, the mixing boards, the mics, and all that just captured it different. they smack right. for boom bap purposes.
you could absolutely layer them with any drum, 808's you can layer with anything. there are no real rules as far as layering, you're just trying to create the desired drum sound. like if you got a deep booming 808 like the kicks in this beat
beat drops at 32-33 seconds. the kick drum is a huge 808 layered with a normal punchy kick.
then at :49 seconds the 808 keeps playing. still booming, but the punchy kick was taken off.
then at 1:04/1:05 the punchy kick comes back in, like the beat drops more official.
so basically you can use layering also as a way to change it up a little while keeping everything else the same. the listener pulls back like aight, its still banging, and then BOOM BOOM its back and your back up and next thing you know you're busta rhymesing head first off a stage hype as shit