If I remove turbo tax from my computer after I have filed will that impact my ability to file next year. I'm paranoid about keeping it on the hard drive.

Are you using the Desktop program or the online version?  You can remove the program.  You can remove the .tax2020 and pdf files.  But you should back them up and save them to a flash drive or something.  They are your tax return.  And you will need the file ending in .tax2020 to transfer into next year unless you used the online version.