07 jeep gc, esp/bas light is on steady, the cruise doesn't work. Are these related

have vehicle for trouble code

check and test abs system and or hubs for failure Finally Fix Mercedes class ESP ABS BAS FAULT LIGHT Malfunction

code p 0710 refers to transmission fluid temperature(TFT) sensor ---circuit malfunction===causes --wiring--TFT sensor--ECM---TCM
overheating transmission oil leads to early transmission failure so I would not let that slide as for the abs , esp and bas lights I would be looking for another code that refers to a bus or can fault which is wiring or communication problems
Again any lights on are an indication of future costly problems so get it checked out at a professional service center

that means scan it, the operators guide says, get it serviced
so what is the question, how to service car, for this.
RTM
read the FSM factory service manual yet,
can be bad brakes.
scan it,

Have to check for codes & diagnose them, to find that out

Obviously you have a system fault

Nothing new there,same as all vehicle problems

Work on it,find a problem

You must have the systems scanned for fault codes before any reason can for the problem can be given.

I had this same problem with my Jeep Liberty 2008 and it need a new computer
module...it was very expense thank the Lord that I was still under warranty.

take to auto sparky-sounds like solenoid

You need to take the jeep to a dealer or a good mechanic who can retreive the codes out of the computer. You may have a module problem but I will not guess without knowing the codes.