Whom ever put the "do not remove" sticker on that knockout wasn't even smart enough to get it right side up. I'll bet there's just another breaker socket under it.

Code requires that the feed be large enough to run everything at once. Licensed electricians have to follow the code, as should anyone. ... However, you could just hook up your drier to that 50 amp breaker for the range and just not run the range and drier at the same time. Or add a breaker and just not run the drier and one of the other big ticket items at the same time. I have to do this in my house because while it has about a dozen breakers, apparently all of the things in the house are hooked to just one of them...

Also, those appear to be GE breakers. If you have nuisance tripping problems, try swapping them out for Square-D HOM series breakers. They are much higher quality and won't trip when they should not.