1. Yes, it's fine, and also perfectly natural, to begin a sentence with 'And..' in an informal email.
2. No, ‘I want you to come and could you bring some sandwiches’ doesn't work.This is because the structures either side of the 'and' are so different. You could make two parallel clauses, both as statements, like '‘I want you to come and I wonder if you could bring some sandwiches’. Or, if you want to keep it as a question form, you'll need to put 'Could you bring some sandwiches?', with a question mark at the end, on its own.