Can you use 16g s/o cord from the j-box to a 2x4 highbay fixture. the voltage is 277 volt & is a fluoresent fixture.

With LED lights, one bad one can make all the fixtures on the line behave strangely. This is a warranty / technical issue. Contact them direct for warranty support and exchange.

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Use an oversized AWG cord, e.g. #12, #10 AWG to avoid voltage drop in the cord. I guess each unit needs 5 amps for total of 10 amps when both run at once.
With a 14 Gage cord (0.5 ohm @ 200' wire) and with both units starting up at same time, the current (amps) draw is 60 amps (6x running current) and 1800 watts, the 1800 watts consumed by the cord, this power dissipated as heat. The 1800 divided by the 60 ( watts/amps = volts) years a voltage drop of 30 volts, at start up of the two compressor motors if at 5 amps flc (full load current). This scenario with a 14 gage, 100' cord is problem bound so a thicker wire cord is needed to keep voltage drops within 10% of the load's rated voltage. Use a 10 or 12 Gage cord or two separate cords.

I am seeing that this tstat says it handles 24-277 volts but when specs are pulled this tstat is a high voltage tstat. Obviously it could be done but what you really need is a simple 24 volt tstat wired to r and w. You can also get a tstat that doesnt have batteries if you wired in the C terminal.

Take the end cap off the fixture case - unwire the old socket and reverse the process for installing a new socket.
The little slots on either side of the socket slide onto the fixture case.

Kill the power at the fuse box, remove the light fixture and make sure your wires are not shorted behind the fixture... usually happens when they are bunched up in the electrical box and squeezed.... could be a fire hazzard

first you need to know that the ballast is 277 volts or you will fry it, 120 volt ballast will not work on a 277 volt system, i suggest that you need to get an electrician to help you with this, if you hook it up wrong it will cause a problem

The terminals you listed are correct.
T4 -T7 mated
T5 -T8 mated
T6 -T9 mated
10, 11, 12 combined connection

L1, L2, & L3 = output / line leads

However you should have 277 VAC line to ground and 480 VAC Line to line (Across any 2 phases)

So terminals 1, 2 or 3 to ground should be 277 VAC (L1 L2 or L3)
1-2 or 1-3 = 480 VAC
any combination of
1 , 2, or 3 to each other = 480 VAC

As a "generator man" with 19 solutions one being "You might have to sting it" you should know this and be able to use the diagram on the power head to get your desired voltages unless the wiring data plate is missing. I have had to dial in voltage regulators when switching between 240 and 480 to prevent automatic shut downs from over / under voltage.

Kelly

If you want two fixtures to be operated by the same dimmer, it is easier to just connect the fixtures together by twisting leads together and then wire nutting them and then run one set of leads to switch. That way you meet all codes.

Install one dimmer at the load end feeding the light. Install a standard 3way switch at the other end. Make sure the dimmer switch is rated for the type of bulbs in the fixture. ie Led, halogen etc.

Certain dimmers can control standard incandescent lamps that use 120 volts while other dimmers can control low voltage xenon or halogen light sources that use 12 or 24 volts.