Does Exiling a Creature Remove Counters?
Counters Are Not “Removed”; They Simply Cease to Exist. See Rule 400.7. Rule 704.) in Short, the Exiled Permanent Becomes a Non-Permanent Card That Is a New...
counters are not “removed”; they simply cease to exist. See rule 400.7. rule 704.) In short, the exiled permanent becomes a non-permanent card that is a new object, causing all statuses, counters, equipment, enchantments, etc to detach.
Does transforming a creature remove counters?
Yes. Nothing has entered or left the battlefield; all that's happened is a creature's characteristics have changed. This does not cause it to lose counters, Aura, equipment, etc.
Can you regenerate a creature with counters?
You cannot regenerate a countered creature.
Countering a creature spell prevents it from entering the battlefield, so it never had an opportunity to be regenerated. Furthermore, Regenerate prevents the destruction of a permanent, but countering a spell doesn't destroy it.