It is well and truly time to replace a 10year old domestic router of any brand. In fact it is about 5 years overdue.
Just for your info..
There is no firewall in the airport extreme.
Some people call NAT a firewall.. even Apple.. but it is not a true firewall.. and it cannot be turned off.
Tell us a bit more about your Internet service.
Who is your ISP?
What make and model modem?
Is it also a router?
Do you have double NAT? There will be a problem listed in the airport utility on your AE if that is the case.
Could your ISP be running a proxy. That will stop TV streaming.. you might need to ring your ISP to find out.
Or they could use what is called CGNAT which won't show up as double NAT but is still really double NAT and acts like a proxy.
My recommendation is to see if you can borrow a non-apple wireless router and see if that fixes the problem.. if it does then I would also tend to recommend you go with a new non-apple router.