Here is a good pattern http://www.russianlessons.net/grammar/nouns_gender.php :)
I can add only that if a word ends with "шь", "щь", "жь" or "чь" it is feminine. And if it ends with "ш", "щ", "ж", "ч" it is masculine :)
And also there are a few neutral words (время, имя, пламя... ) ending with "я".
Starting to see how Ukrainian and Russian are similar яблуко (Ukr.) and яблоко (Rus.). I try not to confuse them although I hear that both languages are mixed in a certain dialect in Ukraine. That's also why I'm learning both on Duo because nearly all Ukrainian speaking people can speak Russian too. I've also heard that Polish is even closer to Ukrainian than Russian.
There is no such correlation. Яблоко (neuter), груша pear (feminine), огурец cucumber (masculine), морковь carrot (feminine), хлеб bread (masculine), масло butter (neuter), молоко milk (neuter), вода water (feminine), чай tea (masculine), кофе coffee (masculine), соль salt (feminine), перец pepper (masculine), мясо meat (neuter), курица chicken (feminine), колбаса sausage (feminine), etc.
However, you can find that the nouns with -о ending are neuter in general.