No, you can't shoot everything. You CAN shoot 3" or shorter shells. Inserting a shell longer than the chamber calls for is not quite suicide, but certainly qualifies one for the Darwin Award semifinals.
Being an 870 it'll probably hold together, but not repeatedly.
As for slugs, the only things a 3" slug will do that a 2 3/4" one will not is go through your money and build a flinch faster.
There's few hardnfast rules on slug selection. Here's a few loose guidelines....
Smoothbores and full diameter slugs like the older Forster types and various Brennekes go together nicely. There'll be one that's best in a given shotgun. Buy 5 packs and bench test them until you find the tightest grouper. Then buy lots of that.
Fully rifled bbls and the sabots usually work together best.Again, you have to find the right combo.
All 12 gauge slugs are very effective on deer sized game, even big Michigan whitetails or our Eastern Shore cornfeds here in Md. For bigger game or stuff that bites back like hogs, the Brennekes seem to be best.
Open chokes are USUALLY best for slugs, but which choke is best is up in the air.
Lots of stuff in the Archives...