I don't know. Some people have reported problems installing old versions when a newer one is, or has been, installed. You havent said which OS you're using. Max 8 probably won't work on Vista, may work on Win7 in XP compatibility mode.
The license should stay there, but will only be valid for the version which installed it - 2010 won't work with a Max 8 license. And there's no difference in the software between a trial and the full version - it's the license which determines the type of installation (commercial/student/trial).
Remember that a trial is only valid for 30 days. After that Max will not run (unless you buy a license, of course).
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).