Netgear DGN1000 - Is mine faulty or is this how it works?

I have both airtel and bsnl broadband connections at my place. For airtel i use beetel + a wifi router and bsnl a tp-link wifi modem. Recently I purchased a netgear dgn1000 to replace my airtel modem + router. I setup the router with relevant user id, password, vpi setting etc. But I noticed a few problems. First is that it takes over a minute to show it has established a link with airtel line [with the beetel it was instant]. After connection is established lots of sites didnt open. I changed the mtu number to one below its default [1492] and most sites open. Another problem is some sites wont open initially and when you click try again on the browser window it would connect. I use thunderbird email client to check mail. Almost every time I used to get unable to connect to server. After many tries it used to connect. I never faced this problem with beetel modem. I felt maybe its a problem with airtel line and tried this router with bsnl and over there too same problem! I tried tweaking the settings but no luck! I updated firmware to latest. Another interesting thing is under router status my beetel or tp link used to show good snr and line attenuation numbers but with netgear it is showing different numbers indicating high amounts of noise in my line.

I want to know if any of you have the same router and facing the same problem or is mine faulty due to which this is happening?

Showing a marginal difference in noise levels is normal but as you said there is a considerable difference which I believe indicates some problem with the new hardware. Have you tried cleaning the terminals?
Having to refresh a few times could have been an issue with the DNS you use with the new modem. If they are different from the old modem then try the old settings and see if that makes a difference or try Google dns : 8.8.8.8 and 8.8.4.4

If these things dont help I would suggest you ask for a replacement or a full refund and purchase another brand.