You specifically mentioned 32bit processing and output, just for safety, does this also include input, too?
If the input is 32bit, then yes.
How can I change ST profiles during processing, i.e. have 3 files using a different profile each?
Use separate watch folders for each processing preset. This is a feature of WatchCat Professional though (so it's a paid feature). If you don't have a license it'll insert beeps in the processed sound if you use more than one watch folder. Or manually change the ST preset of the first watch folder, but it's not really batch processing then anymore.
When I change the content of a profile before a file is processed, will the changes apply or does WC cache the original profile for the complete session?
If I remember correctly the preset is determined as processing starts (so if a file is pending and you change the preset, once the file starts it'll use the new preset; I'm not completely sure though).