There is no specific rule you just have to memorize the word with the article. But I can say that many nouns that end with E are feminine

Apprendre le mot avec l'article ! Toujours apprendre: un chapeau, une casquette... Apprendre le genre est irréalisable.

I agree, not necessarily any logical rules, so you need to memorize the gender with the word. Consider this: French words (as well as many other languages) are made up of 2 parts: the word and the gender. If the gender is wrong, the whole word is wrong!! So be sure to learn the gender with the word. This makes a huge difference with some words, but in general, people will be nice about it if you say the wrong gender. To help you, make sure to frequently use new vocabulary to help you get a feel for it and if you become more comfortable with it through practice, you'll rely less on guessing!

Probably in the same way that you remember all those Chinese characters. If you say "un table", I understand but it seems odd because I know that it is "une table". Don't search a logic, there isn't. Don't loose your time to try to remember the gender of each word and keep learning naturally by reading and listening. You will never be judge if you have the wrong gender. Actually I have the same problem with dutch and its neutral gender.