oil pressure or pump help

ok so i have a 01 1500 with a 6.0/80e swap... its been in the truck and running great for about 4 months, the 6.0 has a factory oil cooler and the people that pulled it from the 2500 cut the lines about half way, so i looped it when i put it in the truck and have had no problems until now.. well the other day with it being cold for the first time i guess somthing shrunk, and pulling out of my front yard to go around to the drive way it came apart about half way around so it was started and lubed for about 20sec.. my check oil pressure light came on and i shut it down a few seconds after.. truck never went over 1500 just enough to get it moving and engine was completly cold from sitting 3 hours in 20degree weather so heat on anything wasnt a factor.. went and got mag light to investigate and found problem, next day took 3-4 qts to get to full mark so it was only 2-3 from low mark which i think is good because it didnt run completly run out of oil & theres a trail up to where i shut it off at... now after fixing hose and adding oil my oil pressure at idel when cold is 34psi from idel-2000 but when warm from idel-2000 is 55psi and gos above 60s when getting into it..my main concern is when its cold it will flutter up and down between 30-35 while driving, i havent drove the truck much since swapped or with it ever being this cold so im not shure if its the temp or if possible i damaged the oil pump if thats possible.. once warm it hold steady with no fluttering, any input?

it shouldn't go up and down at idle unless your rpm's are. maybe do and oil change with a better oil filter and remove those rigged oil lines / and install a bypass plate if your not going to use a oil cooler. that oil pressure seems about rigth for a 6.0 maybe a little low at cold idle make sure those lines are not crimped / restricting flow.
maybe the hose that u used for connecting them together is crimped

i changed the oil on it about 400 miles before this happened and now it has 4qts of fresh oil so its manily new, i run castrol 5w-30 with a wix filter. i plan on getting the block off plate if i can get my buddy to let me get it off his extra motor.. the line isnt crimped, where they cut it i have about 3 inches of hard line and the other side is soft so i just slid it over the hard line and clamped it...

I have 01 Tahoe the oil pressure gauge does the same thing when cold. It does have a million miles lol 200600 miles. Not as cold her in San Antonio. I notice this happening when the temp reaches under 50 degrees in the AM hours.

good to hear, like i said i havent drove it since its been cold so i have nothing to compare to.. i also noticed that until it gets abot half way to warm it dosent really move from the 35psi when the engine is reved unlike when its warm it will go from 35-65 depending on the rpm