There is no difference where to put your cable modem (gateway) in the house cause usually every room is wired with coax cable. It doesn't matter if you either place your modem in the basement or include extra splitter in the living room near your TV. As long as you use approved splitters (5-1000Mhz at 3.5 loss per output) your signal levels and noise ratio should remain the same.
Yes that's true but you seem to be talking about a house without ethernet wiring - that's far too Amish for me.
If a house is wired with ethernet it will all terminate in one place. That is where you want to put your networking hardware especially if you have lots of equipment. I have my cable modem, my router and my 24 port switch. I don't want all of that stuff sitting in my living room or dining room which is the most central spot in my house nor do I want a panel with a dozen or more RJ-45 jacks for all of my ethernet cable runs. This stuff should go in a discreet location like the basement or a closet.
Once set to Bridge mode, the modem acts as a modem only. You can set that mode your self, or, you can ask tech support to set it. In that mode, you can apparently get two IP addresses, which means you could in theory run two routers (two networks) behind the modem.
You don't have to go to bridge mode to use a wireless router behind the modem. You can set the router up so that it has an IP address that is outside of the IP address range of the modem. That way once its all connected and running you can still log into the router if any changes are required. You would also turn off the DHCP server on the router and allow the CGN3 to issue all LAN IP addresses. This will ensure that there are not IP conflicts which would be a problem in any port forwarding situation. Once that is set, turn off the wireless on the CGN3, connect and reboot the router and you would be set to use all of the ports on the CGN3 as well as those on the router, and connect via wireless to the router.
If you decide to go with bridged mode, I highly recommend the ASUS RT-AC68U router. I bought a CGN3 back in early November because I upgraded to the Hybrid 150 plan and decided to go with bridged mode. A couple of days later, I ordered the ASUS online and it arrived within 2 days. You will not be disappointed with the ASUS. I also have a solution for logging into the CGN3, which was provided by Wayner92 (thanks again Wayne)! Without that, you won't be able to log into the CGN3. I do it every day just to look at signal strength readings and firmware versions, plus anything of interest in its log.