Is it possible to have HTTPS connections over proxy servers? If yes, what kind of proxy server allows this?
Duplicated with How to use Socks 5 proxy with Apache HTT
I don't think "have HTTPS connections over proxy servers" means the Man-in-the-Middle attack type of proxy server. I think it's asking whether one can connect to a http proxy server over TLS. And the answer is yes.
Is it possible to have HTTPS connections over proxy servers?
Yes, see my question and answer here. HTTPs proxy server only works in SwitchOmega
If yes, what kind of proxy server allows this?
The kind of proxy server deploys SSL certificates, like how ordinary websites do. But you need a pac file for the brower to configure proxy connection over SSL.