I would say "Yes", you are right to 1 and 2. But also any other weight you add to the trailer between the trailer axle and hitch will add to the tongue weight. The closer to the hitch, the more of the additional weight will be on the tongue. It's proportional; if it's loaded half-way between the axle and tongue, half the additional weight will be on the axle and half on the tongue.
And for 3&4, yes, add the tongue weight to the vehicle payload. The vehicle's total GVW which includes the trailer tongue weight, passengers, gas, and whatever else you've added to the truck/SUV should not exceed its GVWR.
If you add a WDH, things get a bit more complicated, as it can transfer some of the tongue weight back to the trailer.
And the same applies to the trailer. You do not want it's total GVW to exceed it's GVWR.
The total trailer GVW is split between the weight on its axle GAW and on its tongue. The trailer's GAW should not exceed it's GAWR. The tongue weight is carried by your Tow Vehicle.
And you can also consider the TV's front and rear axle weight ratings (GAWR).
You really need a scale to get into GAW measurements.
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