start at a corner when pulling it - you will be buying new pad, but that is cheap ~ $2.75 - $3.25/yd. It gets stapled down and will probably come apart as you try and remove it - not worth re-using and having it bunch under the carpet - several different weight pads - if yours was decent quality it's probably 8#.
It's the insulated line that looks like the leaker? Think it's from the circulating hot water i think you mentioned once? Also looks like insulated line from an external AC unit. Any chance of isolating that section of line to see if it dries up? No major wet spots on the ceilings? hole must be in the wall cavity - if so go slow on pulling floor....