Is it possible to have a maximum number of a specific merchandise?

...and even let it count down when it's ordered and paid?

No, there is no quantity parameter or usage for merchandise (or any plan type for that matter). Subscriptions can have a number of renewals per user, but no usage limit. Best you could do is use CBSubs SQL Actions to count the number of merchandise purchases and if is equal to or greater than the quantity you want then you'd disable new purchases for the plan. Example query as follows for this (note this is untested and is just an example).

In the above you'd replace QUANTITY_HERE with 5 for example to limit the number of purchases to the plan to no more than 5. It dynamically fills in plan id via substitution so you can basically copy paste, set QUANTITY_HERE, and should be good to go ideally.

Sorry to dig this out, but I have a similar question. I see now that CBSubs does count, on top of a plan I can see two lines
Merchandise records with this plan 3
Completed merchandise with this plan 3
Can I use this number somehow to automatically switch the config of this plan to
Allow new subscriptions = No
? Maybe using an auto action? Something like, on cPayUserStateChange if number XY = 20 then set Allow new subscriptions = No?

Second question: I guess there is no option for a "Sold Out" display?

That's just counting the rows. You'd need to write a query that counts the rows then toggles off new subscriptions. The update query above does this for you already.