you are right! The only bombs ever used for real were the two on Japan, and they were fission only low yield bombs.
Basically the two on Japan had an approximate yield of 20kt, although studies afterwards estimate the actual yield was probably less, around the 10-15kt area.
What we call thermonuclear h-bombs are basically fission induced fusion (hydrogen) bombs. The fission part could be seen as the trigger or starter for the much more violent fussion part.
The largest I've ever heard of was a 100mt h-bomb, approx 10,000 times more powerful than those used on Japan! Scary.
Typically these days warheads arn't just made as powerful as possible, warhead engineering designs bombs to be more effective, this might mean making it contain say 3 smaller nuclear bombs rather than one massive one = more effective.
The testing thing is a bit hypocritical, the USA have done soooo much testing (mainly back in the 50s) that it is untrue.
N.Korea is developing its own now and basically wants to test them like the USA did many years ago.
Whether we can trust them to use them for peacekeeping defence is another issue altogether