Anyone knows a professional carpet cleaning company here in CM, and if, what are the costs?

Alternative: Anyone knows where I can rent a carpet cleaning device with the liquids like I used to rent in Europe?

I would check with carpet retailers for their leads. A large seller is located on the south side of the airport expressway between the Ping River and the Airport Plaza; it is next door to a furniture company.

Fore Man beat me to it - worth checking with carpet retailers because others who have asked pretty much the same question have drawn a blank.

A couple of carpet retailers previously mentioned and recommended here:

"Carpet International - On the ring road (Ao Muang ) going east from from the airport: cross over the Hang Dong intersection by the Airport Plaza and go east until you see the pedestrian overpass. On your right (the south side of the road), immediately after the overpass is Carpets International (whose parking lot is also the entrance to a Land & Houses development. Needless to say, you have to be driving west to turn left into the parking lot".

(I think this is probably the same one Fore Man mentioned)

and

"Shop selling carpets, very good quality and not too expensive. If you are coming from Hang Dong towards Airport Plaza, there is a new shop there - just opposite the Jet station"

I would also suggest checking with the management of a few hotels or condo buildings - nearly all hotels have major carpeted areas as well as in the rooms. Could be they employ a carpet-cleaning contractor or have in-house people who could do the work for you?