"When I'm trying to get both connected, I found that I couldn't establish Internet connection via WiFi if I connect the network cable to the Ethernet port that supposed to be from modem to the wireless router."

That is LAN port from modem/router to WAN port Netgear router.
You would need to set up the Netgear with a static address on the WAN port for this to work.

"However, if I connect the network cable to any of 4 Ethernet port (which are meant for computers connected using network cable and not wireless), I could access the Internet."

That is LAN port to LAN port and in this case the Netgear is acting as a wireless switch and it is advisable to disable one of the DHCP servers. See the "How To" Connecting 2 routers together and staying on the same subnet.

"Another thing, I realized that I couldn't access to the console web page of my Wireless Router. I can only access to the web page of my modem router using the local IP 192.168.2.1. The IP for the Wireless Router by default is 192.168.0.1 and I also has been trying numerous IPs but to no avail."

Because the Netgear is acting as a wireless switch the IP address of 192.168.0.1 is not on the same subnet as the rest of the network and hence you cannot access it from that subnet. You could give it an address of 192.168.2.2 providing it is not in the DHCP pool from the modem/router.
See the "How To" for an example.