Some 200 amp breaker panels are made with only 20 slots.
No. You can not buy a 200 amp that only occupies 2 slots on the panel.
If you mean can you put a single 20 amp breaker in an electric panel, the answer is yes. An electric panel is typically made to handle more breakers with values that add up to more than the rating of the panel on the supposition that you will never draw full load on all breakers. If you do the main breaker would trip. In your case you are under utilizing the panel, but this is not a problem.
only if listed in the panel board
No, the Square D designed breaker can only be installed in a Square D manufactured panel.
The dryer is 220VAC. You need a double pole breaker to get 220 out of a home breaker panel. Perhaps you should contact an electrician who understands wiring so that you don't burn your house down.
Only a Square D designed breaker can be installed in a Square D manufactured panel.
You basically have only 2 options:Replace your old breaker box with a larger one.Install a secondary breaker box.Either way is major work and might violate local codes. I strongly suggest having an electrician do such work.
Your question is a bit vague, but let's try a two part answer. If you have a GFCI breaker in an electric panel you should only have one connection at the breaker, but the breaker will protect all devices on the circuit. If you are talking about a GFCI outlet, they are equipped to extend the GFCI protection to other non-GFCI outlets by using the proper "output" connection on the GFCI.
The sub-panel need to be fed from the main panel, by way of a circuit breaker connected to one of the breaker locations. Or if your sub-panel has a main breaker installed you can feed from the main panel with a sub-feed lug kit. This looks like a breaker, but is only a point where you can branch off the sub panel.
Only if the form factor and specifications are the same. Usually, if it fits and mates with the panel and is the right current and voltage rating, you are okay.
No, if you have a Square D distribution panel only Square D breakers will fit in it.
If the breaker only trips once a week you may have a bad breaker or the breaker may not be large enough for your A/C unit. You should also have an electrician look for any loose connections from the unit to the breaker panel. (It is not uncommon to have a bad breaker)