Do querystring parameters get encrypted in HTTPS when sent with a request?
Yes. The querystring is also encrypted with SSL. Nevertheless, as this article shows, it isn't a good idea to put sensitive information in the URL. For example:
URLs are stored in web server logs - typically the whole URL of each request is stored in a server log. This means that any sensitive data in the URL (e.g. a password) is being saved in clear text on the server