Dunno... I have two R7000 and they both run perfect with ddwrt. Don't see the point of stressing how they fail on stock firmware when ddwrt is there and fully functional. I don't care what software my router runs as long as it does what I want.
Turns out I wanted ddwrt anyway due to my use of...
This is possible, but it would likely require additional equipment. You need a proxy server. One way would be to have your own DNS resolver that simply returns your proxy server IP for all DNS queries. On your router, you could block all outbound DNS and all outbound HTTP and HTTPS from the LAN...