I believe the OP is trying to understand booking rules as they apply as a reward ticket issued by a partner airline.
The yes & no responses are slightly confusing.
Basically what you are trying to say is that when all the "available seats" on the online map are taken, you may be out of luck.
The OP is asking if s/he is entitled to even see and access the seat map and the answer is a definitive yes since the tickets are not classified as Basic Economy. Once the TK award is booked, note the UA confirmation number and access your reservation on the UA website for seat selection.
In regards to the carry on question again the yes & no response is confusing.
It goes without saying that if you are in a later boarding group or if space runs out you will be made to check in a bag. This applies universally to all commercial air travel situations not just UA.
The OP is asking if there are any known restrictions to his/her carry on allowance specifically in regards to a TK award ticket on UA metal that would absolutely prohibit him/her from having a carry on. The answer again is no. You ticket is not subject to Basic Economy rules.
And finally in regards to free UA baggage credit. It is true I was only addressing free baggage associated with qualifying Chase Cards. What I meant to say is that whatever qualifies you for free baggage whether it be elite tier membership or credit card/frequent flyer number, make sure that that your MP number is associated with the reservation so that the computer will grant you those benefits. But yes, those benefits are extended to a TK issued UA metal ticket.