Cooking is hard, whereas eating is easy.
Whereas is a conjunction used to compare the difference between two things. It is most commonly used to mean "although" or "while in contrast" and could introduce a dependent clause.
In the closest definition to whereas, however is a conjunctive adverb used to contrast two independent clauses. You wouldn't use it with a dependent clause in this sense.
I would use however instead of whereas in your example sentence.
Cooking is hard; However, eating is easy.
The punctuation depends on which style guide you're using. Many recommend using the semicolon, but it isn't incorrect to use a period or comma. You would not use a comma after a conjunction, but you should use it after a conjunctive adverb.
You would not use whereas in this sentence, because you aren't showing a direct difference between two facts.
We thought she was going to come to the party, however, she didn't show up.
If you wanted to use whereas in a similar sentence, you would need to compare what we thought with what someone else thought.
We thought she was going to come to the party, whereas they were certain she wouldn't.