Translation:Thank you! Goodbye!
Usually 谢谢 is used. 谢谢你, while colloquial, is actually grammatically incorrect, as there is a redundant word. One doesn't show more gratitude than the other; they mean about the same thing.
Other examples of saying thank you or showing gratitude include 多谢、谢谢你啦 which is colloquial as well, and the formal 非常感谢e.g. 您对我们的支持 i.e. Thank you very/so much for your help towards us (or any acceptable equivalent).
《拜拜啦》 (bài bài la) is used more frequently in Taiwan, and sounds just like bye-bye. I would argue that while 《再见》 is the standard, it can come off as rather formal or vanilla. There are other ways to say goodbye: 明天见 (míngtiān jiàn, "see you tomorrow", use only if you're actually meeting again); 再联系 (zài liánxì, "let's stay in touch", used to emphasize staying in contact even though you might not be physically); and even 有空再聊 (yǒu kòng zài liáo, "When’re you’re free, let’s chat again", very informal). Have fun!
It can be interpreted that way, yes. Even though thats also the literal meaning of the characters, that meaning is implicit in conversation as 再见 it is a common general expression when departing. A similar phase, 再联系, would be more effective in expressing a desire to 'keep in touch'.
I see good reviews for Hello Chinese, although I have never tried that before. The pencil and paper method is the most effective for learning and remembering the characters themselves.
Just a tip, there aren't spaces between each 'phrase' or 词 in Chinese, “谢谢你们。” would do. On that note, I hope this has been helpful and if so, 不用客气; otherwise, keep the questions coming and perhaps someone else will reply with a better, clearer answer.
2020.5.23 Yes, learning to write hanzi, or even just to spell with an alphabet takes a lot of repetition and effort. Otherwise we wouldn't have special checkers or kanji prediction software on cell and PC keyboards
I think one thing if you are a beginner with hanzi kanji, it is good to learn some of the basic characters first. 口，女，金，言，目，月，土，木，食 etcetera since many of the more complex 10+ stroke ones are built from these building blocks.
There will be some hanzi that you'll remember instantly, and others you'll always forget. If you're having trouble some people make a story out of the basic hanzi in the character and remember how to write it that way
Good luck. Learning to write Chinese is way more difficult than learning to just read it