What is the difference between ふさわしい and 適当 ?Feel free to just provide example sentences.

彼女はこの仕事をするにふさわしい

"She is qualified for the job. "

彼女はこの仕事をするのに適当である

This means the same as first one and grammartically correct, but we don't say that. Second sentence may be used in writing.

Both words mean the same mostly, but little bit different.

ふさわしい is always used with positive meaning like

大統領にふさわしい人
(The person who deserve to be President. )

However, people usually use 適当 for negative meaning like

彼は適当に仕事をしている
(He is irresponsible for his work. )

Or

彼は適当にあしらっておけばいいよ
(You don't need to deal with him seriously)