[Mod edit: I have numbered your questions to make answering easier.]
Hello rvandenhaute and welcome to the forum.
A2 You can run the standalone SampleTank 4 ("ST4") program. And create Set Lists as described in the ST4 User Manual. MIDI Program Change messages are used to select the Song and the instrument to be loaded.
A3: Loading times can take several seconds. The best thing to do is rey it out with the free "SampleTank 4 CS" that should be in your User Area / my prodcuts section
A4: The ST4 standalone program only accepts one MIDI device at a time (other users has requested support for multiple devices). You might be able to use some sort of MIDI combiner device to merge the MIDI streams. Or running ST4 as a plug-in in a DAW could be the way to go.
A;so with a DAW you could have 2 or more instances of ST4. One track would receive MIDI from the "88 hammer action" keyboard and the other from the "synth action controller". That might ease any instrument loading issues as you could switch instrument in one ST4 instance while playing the other.
Dreaming a bit further:
-- track 1 = input from the hammer action keyboard, with ST4/piano
-- track 2 - input from the synth action keyboard on MIDI channel 01 with ST4/synth
-- track 3 - input from the synth action keyboard on MIDI channel 02 with ST4/another synth
-- then change the channel on the synth keyboard to select one of the two instruments.
Another way might be to load a Multi (there will be a delay while all the instruments in the Multi are loaded) then use the MIDI channel setting on your keyboards to select the instrument to play.
Download and install "SampleTank 4 CS" using the IK Product Manager ("IKPM")and try it out the different approaches on your system.
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Going off-piste:
You might like to consider Total Studio 2 MAX which is on sale throughout November:
https://www.ikmultimedia.com/news/?item_id=9951which includes a large number of sounds libraries for 25% of the list price
Or, for a Hammond B-3:
https://www.ikmultimedia.com/news/?item_id=10103on sale until January 04, 2021.
But don't get them together. Buy one, then you can get the other as a Crossgrade and use the JamPoints from the first order to reduce the price of the second.