"I am lying alone and reading."
Translation:Я лежу один и читаю.
I don't understand why sometimes it's adverd + verb (I've come to see that most of the times it's this way) and others it's verb + adverb. How can I learn when to use each?
It really depends on the adverb. Some adverb work better after the verb, others before it. I suggest you just learn them one-by-one.
There is no real rule, just guidelines. I've translated the guidelines about the adverbial modifiers of manner here: https://www.duolingo.com/comment/11620891