What im trying to figure out is that if I were to build something on 2013 in my house would it work on school computers that are running Inventor Pro 2011 or 2012.
No it would not, once a file is saved in a newer release you can not go backwards.
Regards
Martin
What if i where to start in an older version, would i be able to edit the file in a newer version ?
You can create the model in the older versions (2011 / 2012) and then edit it in 2013 - but once you have saved it in 2013, there's no going back.
Yes, you can open and edit an older file type in a newer Inventor version. But saving the file in the newer version will migrate (update) it to the newer version. Saving to a neutral file format like STEP will help with this but you will lose modelling data (extrusions and such).