I don't have experience with ETD and/or MS3. We always do single MS2, as the vast majority of software deals with this type of experiment. Literature has always shown that MS2 yield is higher than ETD or MS3, although reach method can identify specific cross-links

Keep in mind that usually, cross-linking software are designed specifically for each cross-linker class. So, choosing one or another will drive you choice of software as well

Oh, OK. Cleavable cross-linkers have the advantage to be used in searches with large database, but they are a bit trickier to acquire good data. If you have a single complex, composed of a dozen or so subunits, non-cleavable works just fine and they are easier to get good spectra.

If you just want to stabilize your complex, basically any cross-linker will do the job. The different characteristics they present will only make a difference if you are going to identify the cross-linked peptides by MS after the reaction.