Is it possible in any way make webproxy connect to Internet via multiple WANs, depending on request source address?
For example, requests from local network form 10.0.0.1 goes via 172.16.1.1, and requests form 10.0.0.2 goes via 172.16.1.2?
No, it is not. The proxy connection to the Internet is completely unrelated to the connection from the client to the proxy, and you cannot make routing decisions for the former based on connection details from the latter.