Huge question, but there's not really a lot of data to go on. There do seem to be some things that are a lot easier to learn when you are very young.
> why is it easy for me (as someone who grew up in the East) to learn guttural sounds of Arabic
It all has to do with the speech sounds you're exposed to when you're young.
> Does the writing system affect speech, and if yes, then how?
Probably not. Very little if so. The main effect would be preserving old speech forms of the language to some extent, if the writing is phonetically based.
> What are some known neuroscientific tricks (for adults, not kids) for acquiring specific languages?
The most important thing is lots of exposure and practice and also the way you're practicing the language should be as close as possible to how you will actually use the language. There aren't any massively effective shortcuts.