Please help me with my access point setup :(

The reason I said WEP is less secure is that it is now an old security standard and can be easily "cracked" by someone if they wish to do so, however in a home environment that shouldn't be an issue as the attacker would need to have the right software and have a reason to attack your network. If all you're doing is making sure your neighbour is not using your internet connection for free then its OK.

I must confess its a long time since I have used wireless repeating so a lot of my instructions are from memory or a general informed guess so please bear with me

Yes the DNS on the AP needs to be the same as the 2wire (this assumes the netgear is NOT getting its IP settings via DHCP from the 2wire)

The SSID, password and security type all need to be the same on both access points and if memory serves me right they need to be on the same channel too so turn off auto channel if it's enabled. (I think this is why you are seeing two access points in your computer)
Also turn off auto RF managment (if your netgear has it) under advanced wireless settings as it may be conflicting with the 2wire

So quick IP summary:
2wire IP address 192.168.1.254

netgear access point IP address 192.168.1.(whatever number, but not 254)
Default gateway: 192.168.1.254
DNS server: 192.168.1.254
Subnet mask 255.255.255.0

this is with DHCP client disabled on the netgear. If its not this should be filled in automatically.

MAC address of the 2wire entered into the parent AP boxes in the Repeater with Wireless Client Association menu

Hope this helps.