Is it currently possible to install Drush locally on a Windows 10 PC?
You can install Drush on Windows using composer - http://docs.drush.org/en/7.x/install/

You can get composer from - https://getcomposer.org/doc/00-intro.md#installation-windows

In theory you can manage a remote site with Drush, but you have to have ssh access to the remote server. If you have ssh access, you are better off just logging in and running it on the server. If you have multiple sites across multiple servers, then setting up site aliases in Drush makes more sense.