Yes, you can have the Battlefield 1 before the Battlefield 3. But Battlefield 3 does not need any previous versions to be played before it. But for practice you can have the Battlefield 1 to have more idea about that.
You can also use the hacks like BF1-hack to get ahead, dominate in every match you play, top the scoreboards and get more kills than you ever imagined.

Running the new Battlefield 3 game doesn't require any of the earlier versions, so your problem would likely lay elsewhere. Be sure you have a connection to the internet, and try running the game again. It may need to install the patch software fresh again.