Assuming you just plan to run outdoors above ground get a 10 AWG cord specified for outdoor use. It will be a stranded conductor rather than solid.
Use only AWG # 10 copper.
In North America the smallest size breaker found in a home distribution panel is rated at 15 amps
The biggest circuit breaker in any home is the main breaker located in your main breaker panel that is installed where your electrical service cable comes into your home.
Yes the wire size is larger for that size breaker but will not effect the 30 amp breaker protection of that circuit.
If you are talking about a breaker in a house panel then a 15 amp breaker would be used. It is the smallest amperage breaker that you will find in a house panel.
AWG # 10 wire.
Use only AWG # 10 copper.
In North America the smallest size breaker found in a home distribution panel is rated at 15 amps
The biggest circuit breaker in any home is the main breaker located in your main breaker panel that is installed where your electrical service cable comes into your home.
A 100-A sub-panel would be fed from a 100-A breaker.
Yes the wire size is larger for that size breaker but will not effect the 30 amp breaker protection of that circuit.
If you are talking about a breaker in a house panel then a 15 amp breaker would be used. It is the smallest amperage breaker that you will find in a house panel.
50 amps
Depends on the wire size you are using. If the generator breaker is a 30 amp then install a 30 amp breaker.
The main breaker will have marking indicating size of electrical service, or if it is a fuse system....the fuses will have current ratings. If it is a subpanel, it might not have a main breaker. In this case you would have to look in the panel that the feed is coming from and find the size of the breaker that is feeding it. In either case you must look for the manufacturer's label that will have the maximum current the panel can handle, make sure the breaker feeding the panel doesn't exceed this rating.
You can reduce the breaker size because that limits the current that can reach the main panel. There is no safety issue other than the significant danger in an unskilled person changing out a main breaker.
50 amps