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.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.