Check the nameplate on the service panel. There it will tell you what the buss capacity is. On a 200 amp service nothing in the wiring configuration is allowed to be less than that the service rating. In the market there are 200 amp 42 circuit distribution panels.
50 amps
50 amps
Simple. Your main electrical panel will have a "main breaker". This will be a two pole breaker, usually at the top of the panel. It will have a number on the breaker "handle" such as 150 or 200. This is the maximum number of amps your panel can supply. Most newer homes, 1975 and newer have a 200 amp service.
Its not recommended because your new main breaker will allow up to 100 amps and your old wire can only safely handle 60amps. If you put a 60amp main breaker in the new box, that would be acceptable. No, it is perfectly safe. Because the box is overrated, there is no problem. If the box is the main panel, and not a subpanel, install a 60A main breaker so you cannot overload your service. If it is a subpanel this 60A breaker should be in the main panel.
I am assuming by your description that the panel is protected by a 90 amp breaker and the breakers in the panel when added up is 200. This is okay as long as your 90 amp breaker trips on a regular basis. It is typical for the breakers to add up to more than the main breaker under the assumption that you would rarely be running each circuit at its maximum capacity.
200 amps
Look on the handle end of the main breaker. There should be a number there. That is the amperage of the main breaker. That is the size of your house service.
The sum of the breakers in a panel exceeds the rating of the main breaker in almost all applications. This is because of the design usually anticipates that all devices won't operate at once or at full load. So if you had 100 Amp service and you had ten 20 Amp breakers each happily drawing 15 amps that would be 150 Amps and the main would trip. You need to heavy up your service.
no
When I went to a 100 amp service I could not find a 100 amp. breaker in stock. I used a 60 amp. breaker and have never blown it. The 200 amp you are using can handle up to 200 amps, but if you use a smaller breaker it will only handle up to that amperage. The 200 amp is usally the total amperage of all the breakers comming out of the box. You will probably never come anywhere near using 200 amps at one time.
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.
For a main breaker to trip under these circumstances the rest of the panel is becoming close to its load rating. When the 20 amps breaker trips the rest of the panel is close to or over 30 amps, the 20 amp breaker takes it over the top. What trips a HWT breaker is usually a faulty heating element. It could be the top one or the bottom one.