I have a Suzuki tl 1000 s one cylinder running colder and killing plugs and back firing what must i look for.

Could be a dying fuel pump or just a clogged filter. I'd stay away from 12K. They're red lined @ 11K for a reason.

in the pipe from the tank there is a small wire inline inside filter, pull it out and clean it.

this is either fuel delivery problem. Or vacuum leaks possibly. Hard to say without hearing and seeing it..good luck

since you have a cherry red catalyst surely you have a clogged cat and if you do emission test surely is going to indicate the catalyst. now if the one of the cylinder heads is running rich just confirm whether you have any injector with a malfunction and instead spraying the fuel is pouring the fuel and cause fuel to go through exhaust not burnt and possible that is the reason which damaged the cat.

Have you asked Suzuki?

try to baffle the air coming in through the induction paths, when i was younger i had a cbr600f4 and for some strange reason the forced air from speeds over 60 threw off the air to fuel ratio so much that the bike would stall until i slowed down, i used a couple of strips of duct tape to block about 60 percent of the air passage on the sides near the airbox and it fixed it

Have you got a spark at the plugs?
Are the plugs getting damp with fuel/air mix?

bad fuel, replace bad fuel and spark plugs

OK, the first thing to do is check your fuse box for blown ignition fuse all motors in order to run must have fuel, air, fire, oil to operate. Since this bike was setting up for four months I recommend changing the oil and filters, empty and flush the gas tank remove any rust if present, your carburators will need servicing, empty and clean the bowls replace gaskets clean your jets, charge your battery replace it needed. Check your charging system (ie stator.) for proper voltage output replace if needed. check Automatic timing unit at the chank shaft on lower right side of the bike. this is needed for impulse signal to be sent to the coils to firng in seqence. If no fire at the spark plug the problem is either your ATU or your coils need replacing. Happy riding !!!

Sounds like the bike may have a little trash in the fuel line that goes from the tank to throttle bodys I would check the filter if it has one in line, I would also recommend a good tune up, spark plugs, air filter, oil, etc.