Are HTTPS URLs encrypted

The whole lot is encrypted^† - all the headers. That's why SSL on vhosts doesn't work too well - you need a dedicated IP address because the Host header is encrypted.

^†The Server Name Identification (SNI) standard means that the hostname may not be encrypted if you're using TLS. Also, whether you're using SNI or not, the TCP and IP headers are never encrypted. (If they were, your packets would not be routable.)

Yes, it is. But using GET for sensitive data is a bad idea for several reasons:

• Mostly HTTP referrer leakage (an external image in the target page might leak the password[1])
• Password will be stored in server logs (which is obviously bad)
• History caches in browsers

Therefore, even though Querystring is secured it's not recommended to transfer sensitive data over querystring.

[1] Although I need to note that RFC states that browser should not send referrers from HTTPS to HTTP. But that doesn't mean a bad 3rd party browser toolbar or an external image/flash from an HTTPS site won't leak it.