There isn't a right or wrong. Compression is a tool for controlling dynamic range. Sometimes individual instruments need it, more often not. Similarly sometimes (and more often) some light compression on a bus or subgroup with the whole instrumental mix can make it easier to help your vocals play nicely with the mix.
OT but relevant, a trick I was taught by a pro sound mixer almost 40 years ago was that, when you have the instrumental mix done, put it through a Graphic EQ and take off a couple of dB from the instruments in the vocal range (say 250-2000Hz). Keep it subtle so the instruments still sound okay but this can "cut a hole" to help the vocals sit in with the instrumentals.
On your other topic, insert jacks on the main outs of an analogue mixer are probably more often used in a live situation than for recording...and would typically have a stereo EQ unit on them, used to "ring out" the system to buy yourself a few more dB of gain before feedback. However, they can be used for anything.