1. I came to a site by pc but do nothing, then later I go to that site again but using my mobile and buy 2 shirts.
Google Consider it seperate things as far as i know means (Tablets , Mobile and Desktop) have seperate conversions.As you directly go through URL in mobile then
I dont think Google Will consider as conversion (incase with adwords ad then google count as 1 converted click and 2 conversions)
2. I came to a site by pc and buy 1 shirt, then later I come back to that site and buy another shirt.
yes google will count 1 converted click and 2 conversions
3. I came to a site by pc and download 1 pdf about how to use the product but dont buy anything, then later I come to that site again by mobile and buy 2 shirts
Same Rule as above in 1
4. I came to a site using chrome and download 1 pdf about how to use the product, then later I come to that site again to buy 1 shirt but using fire fox
In this Case Adword will take care of such thing through your Default cookies !
Hope It Help !!!