To be honest I just believe you have some kind of connection issue; all you problems come from the internet side of the game, except of the disc one, which I suggest you to pass it to your hard drive (if able, I'm new to Xbox consoles) and avoid permanent use of the disc reader.
I'd check settings like ports, NAT, WiFi or router ones, etc.
Is there no option to install to hdd ? if so do that for a start. Im xbox so wouldnt know about ps3 install if there is 1.Make sure you have the correct ports forwarded as "Ozhm" suggested If you cant find the ports ill list them for you if needs be although they are all over this forum.2nd you can delete the last update you did and re-install and see if that helps.3rd Make sure IF you have forwarded ports that "uPnP" is disabled as this sort of confuses your modem.Other wise make a static ip address and put this I.P you have made into "DMZ" mode on your router/modem if you have the option.
Theres tutorials everywhere for all of this
First I want to start by thanking you for posting your issues in detail. I understand it can be frustrating to experience issues in a game, so I want to help you optimize your experience and help to prevent or even avoid some of those issues. A lot of your issues see to be related to a connectivity issue. I'm not blaming your internet, but sometimes game require a bit of set up or adjustments to improve your experience.
I would recommend to play on a wired connection, as this may help to prevent data packets and files from being lost or corrupt, as this can happen at times on a wireless connection. If you are unable to, you should adjust your router settings to prioritize your console channel, as having other devices connected can take up some bandwidth as well as lower your console's priority in send/receiving. It is a good idea to power cycle your router and modem, as this can help to free the load on them and in a figurative sense, give them a break. You should also set up a static ip address to help create stability on your connection and help to prevent having to reconfigure your ports in the future. A static ip, is manually assigning your console an address so that, if or when your connection is reset or power cycled, it will remain the same and the ports won't be forwarded to the incorrect device. Lastly, to configure your ports, you should try the methods outlined here. When setting up your ports, only use one of the three recommended methods (UPnP, DMZ, and Port Forwarding), as they are all methods to set up your ports and can override each other. Also be sure if you use Port Forwarding to disable the other two methods as well. Should you choose to manually set up your ports the following number should come in handy:
80, 443, 465, 983, 1935, 3478, 3479, 3480, 5223, 10070-10080 TCP
3478-3479, 3658, 10070 UDP
Call of Duty Ghosts Console Ports:
80, 81,443, 3074, 5223 TCP
36081, 3074, 3075, 3478 UDP
I know that is a lot to take in, and I explained it to the best of my ability. If you get stuck or feel uncomfortable setting up your router, you may call your ISP as they may be able to walk you through or even do it for you if your lucky. Let us know if that helps!