Yes, you used "moreover" correctly, and "besides" would be fine, too. Your first two sentences need to be combined into a single sentence, though: "You should buy this dress because it is cheap and beautiful." (When you use "because" to connect two ideas, they both need to be in the same sentence, so you can't put a period before the word "because" here. A comma would be okay, but in this case it's better without one.) Also, don't forget to use spaces around quotation marks and after periods.

As others have said, can use either, but "besides" is better. "moreover" sounds too grand for an informal situation. An english person would be more likely to say "it suits you" if you mean "it looks good on you".

Correct, "besides" also will do.