Since my site is using HTTPS and my proxy is using HTTP, is this a problem? Please explain if this is secure.
This can be secure.
The client can issue a CONNECT request to the proxy, which basically creates a tunnel between the client and the destination server. This way, the client can set up an SSL connection through the proxy, and the proxy will see encrypted traffic. Even if someone else impersonates the proxy, he will only see encrypted traffic.
Another possibility is to do a GET request to the proxy. This asks the proxy to retrieve a page on your behalf. This is usually only used for HTTP traffic, but may also work for HTTPS traffic. If your client uses this method to retrieve a page, the proxy can view all data. Furthermore, a man-in-the-middle attacker may impersonate the proxy and also see all data.
If you use an HTTPS connection to the proxy, it is much harder for a man-in-the-middle attacker to impersonate your proxy.
It also depends on your definition of client too. As you would code something(not a known browser) to not validate the given certificate and that could be a kind of self-signed by the proxy you mentioned.
But as the client doesn't check the stuffs, proxy could fool the client.
Plus keep an eye over the redirects, you may ask for facebook.com(assume no HSTS yet), but the result could be redirected to something like
fb.example_proxy.com even in https with a trusted certificate. So as you don't take about the path you had redirected, the proxy now can have the data you think you are sending to teh facebook.
I had some issues then with the firefox, where firefox marks some completely secure with trusted certificates as insecure connections(even google.com). I mean even a legendary client like firefox could come with this kind of bug, and also it could be vice-versa.