AFCI's would not be required for the heater or dryer, only lighting/receptacle circuits. There is no limit on the number of receptacles on the circuit, however, 23 is MUCH more than I would put on one single circuit.
Answers based on the National Electric Code. Always check local amendments.
@AllanJ: do I need to mark feeder wires in each box somehow (in case someone else need to do electrical work in the basement)? Also - is there any "unofficial" rules on how to run wires to each switch box (for example - feeder wire should always come through top left hole, etc). )?
No rule about feeder entering from the top left, etc.
Marking of the cables is needed here only during the time you are connecting things up. Just to keep the switches and cables for the different banks of lights from being confused with each other. If the labels are still readable when you are done, no harm leaving them there.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.