A small company may be just a one man operation with limited stock of parts, so response times could vary more. The more "boutique" or "exotic" the longer the wait time I'd expect. Assuming the parts are in hand, the time from them receiving and shipping the unit back out should be no more than a week or two. But accounts of customer service ranging from shipping out an entire replacement unit before receiving the faulty one, to "gone out of business" (after they have your money).
Payment should be based on the terms of the warrantee.
It'd be nice if the company notified you of the possibility, and any cost, for upgrades at the time of repair, but not required. Unless you've become a "difficult customer to please" I'd expect them to try to earn more of your business with an offer to upgrade.
Especially in this day and age, the rule is that everything should be put in writing.