First of all, any searches for answers will need the correct identifier, in your case MacBookAir4,1.
Secondly, your issues are most likely due to the low amount of ram of that model. The 2GB version probably won’t install/run at all and a distro like antiX would be a better fit. The 4GB one might run ok, in any case I’d download the Xfce minimal version.
Search the forum, there are a number of posts addressing the issue
Could not install with only 2GiB of RAM - #19 by linux-aarhus .
Minimum H/W Requirements - #4 by ydar .