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On your truck's capacity are you sure you've specified it correctly? F-150s have two different trailer tow packages, the "tow package" and the "Max Tow package." The max trailer weight of 12k corresponds to a truck of your configuration with Max Tow and RWD (4x2). Is your truck a 4x2 or 4x4? In my searches 4x2 trucks are rare as hens teeth. A 4x4 truck in your configuration may not have the Max Tow package but it appears the 4x2s all do.
Secondly your Max Payload doesn't look right compared to your stated GVWR. Payload is the difference between GVWR and the vehicle's empty weight. There's no way your truck weighs 3500 lbs empty. Either your GVWR rating is wrong or your payload is wrong. Read the labels in your door jamb area. Also the GCWR (not another V) you list is correct for a 4x2 truck...verify configuration.
For tongue weight your 900 lb estimate is about right but it could climb to as much as 15% of trailer weight. Given trailer's GVWR of 1200 that could reach 1,080 lbs. Tongue weight becomes payload to the tow vehicle. Verify you'r truck's GVWR and payload capacity. For 1/2 ton trucks outfitted for towing the real towing limitation is having sufficient payload capacity to carry tongue/pin weight plus passengers plus cargo.
I don't think you can get an unqualified answer to your two concerns without verification of your truck's configuration and the rating labels on your truck.
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