Yes, Connection -> SSH -> Tunnels in Putty connection options. Add a dynamic tunnel there. Start the session. Then enter 127.0.0.1 and the port you've chosen

Yes, Connection -> SSH -> Tunnels in Putty connection options. Add a dynamic tunnel there. Start the session. Then enter 127.0.0.1 and the port you've chosen as a SOCKS v5 proxy in Firefox options. Congratulations! Your poor man's VPN is ready :)