1. Yes, Minit should work just fine with other plugins as long as you don’t enable competing concatenation functionality that is provided by W3 Total Cache, for example.

2. Transients are used only for caching the list of enqueued files and their versions and have an expiry of 24 hours. Currently WordPress doesn’t remove the expired transients automatically so you must use a plugin such as Transient Cleaner or Delete Expired Transients to do that.

3. It is not possible to delete “expired” files because there is no reliable way of knowing that they have actually expired and will never be used again. You could add a cron job that deletes cache files that are older than a week or leaves everything but the 50 latest files in the cache folder.