There are some car seat manufactures and vehicles that approve both LATCH and seatbelt at the same time, but this is a very rare thing and generally speaking you either do LATCH or seatbelt but not both. One exception that comes to mind is the newer Ford Expedition. If you check the owner's manual it's quite the chart to see which seating position, direction (forward or rear facing) and weight will allow both, assuming your car seat manufacturer approves it as well. And again this is also all assuming you're using actual LATCH anchors which no 3rd gen ever came with.
The center tether point in the '01-'02 is designed for car seats, however it's not designed for weight pulling back on it towards the front of the truck, it's designed for weight pulling up, which is how the top tether strap it's designed to anchor would be routed. Now I say designed loosely because there's not much to the bracket, but I try to give some credit to the manufacturer as I don't know what type of metal they are using and how much they crash tested it. I would trust it more than a cargo loop though.
Also there are fire stations and hospitals that have NHSTA trained people to check your car seat, but I wouldn't say all or even most do. Just because they're a pediatric nurse doesn't mean they know anything about car seats or their installation. For example, before babies that have been in the NICU can go home they usually have to do a "car seat challenge" where they hook monitors up to the baby and sit him in it for a period of time to make sure baby can tolerate sitting in the seat without positionally asfixiating or something. That is a good thing for them to do however I don't think a lot of them are propping the car seat at the proper angle to match how it's going to be in the car (and make sure the car seat base in the car is at the proper angle). Hospitals here just check to make sure your baby is in a seat before you leave and that's it, no check to make sure straps are at the right height, straps are tight enough, etc.
Installing the base in your rear center seat would likely be the best because usually center is safest and the lap belt is perfect for car seats. If you must install on the outboard seats and your base doesn't have a built in lock off then it should come with a locking clip that looks like this:
Which will install on the seatbelt like this:
I'm a fan of those instead of the seatbelt retractor as it puts the pressure down low on the buckle pulling the seat down rather than pulling up at the retractor. Using the retractor is an approved method though so if it works for you then go with it.
I would double check with that website posted above and find someone through that resource to have your seat checked just as a peace of mind. No matter how good you think you did it, it's always a good idea to have it checked by someone else, especially since most car seats or kids strapped in them are done wrong and they are your most precious piece of cargo in your vehicle. Rock climbers usually have someone else check their harness before they climb up or rapell down, why not have your car seat checked?
