If I were you I would get a bigger anchor and add more chain to your rode, like 50'. On our 10K lb Commander 30 we run 200' of 1/4 chain and another 150' of 1/2" rode, primarily for deep anchorages in BC and southern Alaska. We like the damping that all chain (effectively) provides.
Your...
I don't know this particular engine, but it could be a protective low oil pressure or high coolant temperature indication that's faulty that makes the engine run in limp mode, or whatever the term is for that engine. Usually the system has dedicated switches separate from the sensors that drive...
The only way you can do it with a single drive is with thrusters. Volvo does it with just a bow thruster. I have a joy stick on my twin outdrives and love it.
I get my OMC/Volvo joint venture part numbers here. Drill down to Evinrude, Sterndrive, etc. In the joint venture years the part numbers are the same between OMC and Volvo. The dipstick O-ring is a little larger than the drain plug and overflow plug O-rings.
BPR Parts
I gather the OPs primary question is can the bracket handle the cantilever loads of the outboard out beyond the transom while trailering. I would ask whoever is doing the bracket installation.
Airbags don't change the weight distribution between the front and rear axles. They just reduce the rear sag by stiffening/raising the rear suspension.
You need to pressure and vacuum test the drive to determine where it's leaking. Usually it's at the prop shaft seals, but could be shift seal, drain plug/dip stick seals, or input shaft seal.