Every time I submit my beta application (3 times), I've come acoss a page saying that it cannot be found.. It says something like "this is not the portal/page you are looking for" with a nature background. Has my application successfully been submitted?

First thing, check the email you used, including the spam/junk folder. If you got a notification from ESO beta, then it submitted, and you're good. If not, contact zenimax online and they'll help you out.

I just signed up for the beta and had no issues. I would recommend doing what Dovahkiin: Dragon Born suggested. No email confirmation within the next 48 hours, contact Zenimax.

Try another browser. Firefox worked for me no problems, and others had success with Chrome.

I had this problem many times as well. Its due to the amount of traffic the website is experiencing.
-Use a different browser
-Make sure the browser is up to date
-etc

If you still get the same screen popping up just keep trying every so often (Thats what I did and it got through).

Switched to firefox, got in.