You might find a book Essential Grammar in Use by Murphy handy, all the things you ask about are explained there in a very simple way.

No replace the word "at " with "in" for both occurences. You would use at if you were talking about time i.e. at 7pm on the 15th june 2015. You would use "on" if you were talking about a specfic date i.e. on june 15th And "in" for a month/year "in" june i started....

Hi Vladimir Ok, so first of all, those examples are not the simple and continuous together. They are the gerund form done in the past.You use them well. The only change should be in for at. The past simple and continuous go together when we want to describe two events that run simultaneously: I bought a new shirt while I was shopping at the mall. I I hurt my ankle while I was running in the park. Here are some examples of how we use them: https://askpaulenglish.wordpress.com/2017/03/20/past-continuous-upto-past-simple/ https://askpaulenglish.wordpress.com/2017/01/26/past-continuous-with-past-simple/