How do I get rid of the error?
As far as i can see in this thread, you fixed that problem already but it happened again due to another poweroutage?
You basically just need to do the same again (starting core with the
reindex parameter). You probably just were in the wrong directory, that's why you were told there is no application.
Is the entire BTC blockchain from BitcoinQT available for download as a ZIP?
It is, but downloading the blockchain usually isn't the bottleneck. Processing is the bottleneck. So this wouldn't change much.
And i would highly recommend to build the chainstate yourself and to not trust on others data.
Can I install Win 10 over Win 7 without losing my data?
I am not sure about this since i'm not using windows, but i
believe there is an "upgrade" option which keeps the data.
Even if there is not, you could just copy all of your data (blocks, chainstate, wallet, etc..) to a hard drive and then copy it back after installing Win 10. Then you don't need to downloaded and process the whole blockchain again.