1992 Ford F250 7.3 Diesel hard to start

Yessir.
In the old days, because of the ambient temperature's effect on the crankcase oil and the diesel fuel, often two batteries were used to state the diesel in cold weather.
You might see if there is room for an additional battery on the opposite side of the vehicle from the one that is installed now.
The additional battery can be wired parallel with the one already there, which will not increase the voltage, only the starting amps.
I have done this before, several times.
Another choice is an engine heater, which either screws into the block or is installed inside a radiator hose that has been modified for this purpose.
The cord then is plugged in to an outside 110 volt source, and that will heat the motor oil to ease starting.
God bless your efforts.

get the glow plug checked as a starting point

This is a good engine but they need work from time to time. What is the outside temperature while you experience this hard start? If you plug in the block heater, does the engine start better? Is the engine light on or does it come on at times while you are driving? Hard starts can be related to several different issues. This engine isn't easy to work on unless you have an advanced scan-tool. You need to look at live data and run some tests. The more common failures are clogged fuel and air filter. Dirty ,worn, or defective fuel injectors, low fuel-line fuel pressure, poor oil quality or low oil level, worn or defective ICP sensor, low injection pump pressure, loose or leaking IPR valve, or low compression. These examples should help get you started. You may need to have the truck diagnosed so you know what direction to go in. If you need any additional information, please write back. Good luck.

try a block heater. your engine is cold simple as that. you could try keeping inside a garage where its warmer or plug in a heater. they make a couple types of block heaters or it may already have a heater.

SOUNDS LIKE YOU NEED A NEW GLOW PLUG CONTROLER

you answered your own question with # 1
the fuel leak is doing opposite when starting it is sucking
air . i had the same problem on mine,
it also let the fuel drain back to the tank that then
takes forever to reprime itself
hope this helps

most likely the relay. its located to the left of the fuel filter( looking at the motor from the front). my experience is that they only last about 50,000 miles. the part costs about $20 at an navistar dealer. remove the cowl over the filter, disconnect the batteries(so you don't short the new relay out if you cross the polarity with a wrench) ,remove the four wires from the ceramic relay, un-fasten the relay from the base. reverse the process with the new relay. CAUTION; do not over-tighten the nuts on the wire studs, you could crack the ceramic relay.(iv'e done it) . hope this helps

You need to check to see if your block heater is working if equipped. You also should have a plug to plug in for you heater to heat your dielel fuel.

if it is a powerstroke im sure it does if it is a V10 triton look for a 110v male connection somewhere under/inside the front bumper. if purchased in a hard freeze state it probably comes standard .

are you using cold temperature engine oil!
if not, try changing oil for cold temperature!

hard starting happens due to the cold temperature, air pressure is low during this season so compression inside the engine is low resulting to hard starting!

make sure that all your glow plugs are working.