"Does the tool stay in the hole for the entirety of the...

"Does the tool stay in the hole for the entirety of the pressures/fluid sampling, SWC, and VSP? Or does the MDT get pulled out of the hole after fluid samples, samples retrieved, then back in for the last run(s)? "

A completely different tool string is in the hole for each run. The MDT tool would ideally stay in the hole for the pressure survey as well as sampling operations. On rare occasions I've broken an MDT run into separate pressure survey and sampling runs but that was for unusual reasons.

Sidewall cores are cut using a rotary coring tool and during the VSP a string of shuttles (geophones) are run on the wireline and set at successive stations up the hole starting at TD while firing off an air gun at surface while shuttles are set at each station.