Ok, so I figured it out myself. I will start with PPPoE. To establish a successful PPPoE connection from PC, I first changed my WAN mode in modem from PPPoE to DHCP. This disabled PPPoE from the modem. Then I connected my pc to the modem on the 3rd port and established a successful PPPoE from my PC (from network and sharing centre > new dial-up connection). Now I knew my PPPoE settings work.
Now I connected the cable from the modem to
router to configure it for PPPoE. I went to my router's WAN settings and put my details there. I then connected my router's WAN to the modem's 3rd port. And behold, now my router is the main device and all the features such as DDNS, port forwarding, etc works perfectly.
Another minor issue this creates is the constant blinking of LAN led on the modem. For this, I connected my PC to port 1 of the modem. And then changed my modem's WAN settings again from DHCP to static IP. I assigned a random IP (here 192.168.2.5) from my router's subnet pool and filled all details. (gateway being my router's IP address). In the previous post, I made a mistake that my routers IP address range is
192.168.1.xx, which actually was
192.168.2.xx.
I probably think that the static IP that I provided to my modem doesn't actually affect it and my modem and my router are just connected for PPPoE only. There might be unknown harmless side effects which I am currently unaware of but then again, the blinking stopped which was irritating and the setup is working perfectly fine.
Currently, I am unable to access my modem from my router subnet. It may be because port 3 is hardwired for PPoE only and not for routing. I will put my advances here if any.