NO!
Depends on the size of the wire going to the A/C. If the wire is AWG #10 you cannot install a 40 amp breaker. If the wire is AWG #8 you can.
If the breaker will snap on the bus bar, yes.
Replace the 30 Amp Breaker with a 15 Amp breaker.
Yes. You should use 8 AWG wire from breaker to AC unit.
No, you should not install a 30 amp circuit breaker to a machine which normally requires a 20 amp supply. The circuit breaker is protecting the wire to the machine. That wire is likely only rated for 20 amps, (# 12 awg). Therefore, a 30 amp breaker could allow too much current to go through the wiring to the machine and cause the wire to burn down. Replace the 3 phase 20 amp breaker with the same amperage breaker.
If i understand you correctly, yes there certainly can be. If you replace, say a 10 amp breaker with a 20 amp. you are losing the safety factor - the whole purpose of the breaker to begin with. Always replace a breaker with the exact same amperage rating!
6millimeter square.
Both a 45 amp and 50 amp breaker would require 6 AWG wire. So if you have 6 AWG wire and any devices like an outlet are rated at 50 amps or greater you are okay.
30 amp breaker with #10 gauge copper wire
No. If your AC is currently running on a 30 amp 2 pole breaker, then it is a 220 volt unit. You cannot substitute one 60 amp single pole breaker as you'll only be supplying 110 volts and the AC unit won't work. In fact you could damage it.
You need to look on the manufacturer's specification plate on the unit for the amperage and voltage.
A 20 amp breaker might actually be needed for the installation. It depends on the wattage and voltage of the window air conditioner.