Trailer King Tires

1) To be sure you have enough load carrying capacity in the tires, you need to have individual tire weights because there is front/rear and side to side variation. IMHO, you need a 15% over capacity. It appears you barely have that. So I would suggest a test: Pressure buildup:

You want no more than 10% - excluding the ambient temperature effect (2% for every 10°F).

2) Those tire load tables are MINIMUMS!! You want to be over that! Since tire wear is not an issue on a trailer, a bit of over inflation doesn't yield much in the way of penalties.

3) Wheels are not required to have max load or max pressure written on them (unlike tires!). That's probably because there isn't an issue with wheel failures. The best information I have gathered from wheel designers is that inflation pressure is not the issue with wheels, but load is.

Wheel psi/load rating ID ??
This may be true on rv websites but wheel psi/load rating IDs are a big problem on commercial type haulers websites with lots of split bead seats and cracked valleys are the result of using cheap trailer wheels with no max load/psi numbers. Too many folks just assume cause its a wheel.

OP first question.
Never guess how much load a axle carries. You have the trailer so drop by the CAT scales and find your truck and trailers axles loads.
Never go by actual axle loads for choosing a minimum psi from tire mfg load/pressure charts for trailers tires for many reasons. A couple of good reasons is some trailer are heavier a bit or a lot on one side.
Loads on trailers tires change constantly (side to side/fore and aft) and especially strong side winds causing much higher tire/wheel loads on the trailers lee side.
And of course trailer tires side scrub as the trailer is pulled around a street corner or making sharp turns while backing. Tire on our cars/trucks/suvs/vans do not operate in this extreme environment.
Those higher rated load E ST tires are a good choice for 6k trailer axles.

second question.
Run them at 80 psi cold set and don't worry if they run at 90 psi +. Tire mfg know tires get hot from carrying a load at highways speeds...all is normal.

third question.
If its a 6 lug X 16" wheel then their good for 80 psi. Trailer wheel have load rating some where either stamped or a sticker. These can be on the wheels outside/back side or in the valley. A valley load/psi ID requires the tire to be removed.

last question.
Having made a living pulling non rv trailers using the same axles/tires/wheels that come on rv trailer I've had more cheap OEM tire/wheel issues than any rv'er ever faces.
I always sell cheap off brand ST tires/low cost trailer wheels with no pressure/load ID on CL and go with LT235/85-16 E tires like Bridgestone R-238 commercial grade all steel ply carcass on 6k or 5.2k axles. And purchase a known trailer wheel brand that has a psi/load ID or if the wheel mfg can verify the wheels psi rating.
My 32' rv triler has 10060 lbs on 5.2k axles. I use LT215/85-16 E poly carcass tires. I get 50k-55k miles per set and with three sets running with no issues.

I towed my slightly lighter fifth wheel with TowMax tires for 3 years without incident. I did feel better when I replaced them with Endurance tires which now have gone 2 years without a problem. With your low mileage, you can possibly sell your used tires as "like new" for utility trailer use or something similar.

ApexAZ. Yes, IMO you’re worrying about many things that you do not need to.
If you had 14” or 15” china bombs, I’d be more worried about premature failure than with 16s.
With your loads and presumably 235-80-16 tires, set them at 80 psi and roll!
And don’t worry about the rims.

If you want to really put it out of your mind, go to LT tires.

I'll just add my 2 cents Your stock trailer tires are fine. I always run max PSI that's listed on the tire. As stated, fill them when you haven't been on the road. I carry two spares. I've had all sorts of different tire blow outs using different brands, so it just happens. Some people go years without any tire problems. I've had them blow going slow and fast loaded and unloaded. It's odd I've never have had a flat off roading on some terrible dirt and rocky roads too.