How many breakers in a 100amp sub panel?

You are not getting the answer you want because you are working in an area that you don't have enough knowledge to use the right terms to get the answer you need.

Any panel smaller than the main is acceptable for a sub panel.

The capacity of the panel will be determined by the weakest link.

The weakest link you described is the 50 amp breaker.

Any sub panel must be rated at least the breaker feeding it.

Choosing a 60, 100, or 200 amp panel will not increase capacity

All breakers will always feed either 120 or 240v.

Volts don't go up or down when used.

Amps are determined by dividing watts by volts.

Amps get added to determine load.

Load diversity is the determination of coincidental loads.

Load diversity decides the needed ampacity of panel.

Without knowing the loads, nobody can tell the size needed. I can't imagine how 50 amps would be enough to describe the number of circuits you described. I bet you would need a 100 amp breaker in the main panel, #2 awg feeders to a 100 amp subpanel with at least 30 full size spaces. Most 20 space panels do allow 1/2 space breakers making a 20 space panel capable of 40 circuits, but there is no reason to kick yourself in the XXXXX right out the front door.

Sub Panel Breaker Box

Not enough information. You don't state what your loads are. Your sub feeder size and the number and size of circuits you require have to be based on the loads you expect and whether they can be derated.

Unless we know the load ampacities, no answer to your question would be valid, so ignore what has been posted so far.

Voltage is not the issue here, it is watts and amps. Also, I hope that you are planning to use all 12 gauge wire with these 20 amp breakers that you prefer. You do know that wire gauge has to be matched to the circuit protection. I suspect your 50 amp feeder to the subpanel may be inadequate as well. Again, can't answer that in an informed way without more detail from you.

Twin breakers for the 20 amp circuits should allow what you want to do. These put 2 breakers in the space that is usually for 1 circuit. Go to the electrical supply section of the online retailers and research the panel sizes.

Really depends on the panel purchased. If you were to use 15 amp breakers you could have 100/15= lines, so you would need that many openings in the box plus a couple spares. Just do the math....