First try to use the Microsoft Program Install and Uninstall Troubleshooter https://support.microsoft.com/en-us/help/17588/windows-fix-problems-that-block-programs-being-installed-or-removed
If that does not solve the problem, or if the Troubleshooter cannot repair any problems it found, you might have some Windows files missing. I would suggest
1. check the filesystem for errors (chkdsk c: /f, scheduled for the next reboot)
2. In an administrative command prompt run sfc /scannow
3. In the same command prompt run
DISM /Online /Cleanup-Image /CheckHealth
4. Rerun the above mentioned Troubleshooter
Use the VMware Cleaner from the KnowledgeBase (I believe it's article 1307) to remove any VMware product.
Player DOES support running more than one VM at a time - just not within the same UI. Launch another instance of Player to run another VM.