I can not connect to Tor network with bridges. I set a remote anonymous proxy (as if it is a local proxy) and then tor could connect to the network. I wonder if Tor connects to the first node through this proxy and the connection between Tor browser and the proxy is encrypted.
Yes, Tor connects to the first node over the proxy. The proxy connection isn't encrypted, but the data sent over it will be.
Note that if a simple proxy works, it's likely that other bridges will work too, it's possible that only the default bridges don't work.
A proxy should only be used in situations where it's required to access external internet resources (common on corporate networks) and potentially against poorly configured censorship systems. Note that single hop proxies are not "anonymous" for any meaningful value of "anonymous".