I agree with Michael about usage. He doesn't seem to have mentioned articles though so here are my thoughts:
"I am at sea" is right but you wouldn't ever say "I am at the sea"
"I am at the seaside" (meaning the beach) is right, but "I am at seaside" is wrong
"We sailed across the sea" needs an article
"I lived overseas" (meaning in another country) never has an article and it's all one word
"The bird flew over the sea" takes an article.
"The raft floats on the sea" takes an article
Towns that are near the coast are often called things like "Clacton on Sea", never "Clacton on the Sea"
I'll just add that there is an expression "I'm all at sea", meaning "I'm very confiused and don't know what to do" which might be how you're feeling as you read this and see how random it all is. Sorry. I wish there was an easy way to remember it but I can't think of one, I'm afraid!