#1 the wire size, 20 feet from the pannel to where the heat pump that used to use it was, is whatever size the code calls for. From there to the shop (about 15 feet) is I think 10 gauge. From there to my welder is a 25 foot 4 gauge extension cord.
#2 & 3 the welder and air compressor are the only things on it. The air compressor only draws 16 amps though.
Okay
I will assume 10 gauge wire is correct as 10 gauge wire is rated for 30 amps
continuous loads.
The good news is that NEC (National Electric Code) code allows welders
with low duty cycles (like your Lincoln AC-225) to oversize the breaker on the undersized 10 gauge wire as the welder is not a continuous load device because your current welder only has a 20% percent duty cycle in any setting where it can even possibly draw more than 30 amps. If you look at the older Lincoln manuals it is perfectly okay to power an AC-225 up to 95 feet from the panel with 10 gauge wire and a 50 amp breaker.
THE BAD NEWS IS THAT AN OVERSIZED BREAKER ON UNDERSIZED WIRE IS THEN ONLY SUITABLE FOR USE ON A WELDER WITH A LOW DUTY CYCLE. IN OTHER WORDS IT CAN NOT BE USED TO POWER ANY OTHER DEVICE AND IT MUST CLEARLY BE MARKED AS SUCH. (Even another welder may not be okay - it would depend on amp draw and duty cycle of the new welder to verify the specs still fit within the permissible NEC formula).
So What does this all mean
A) For $10 you could easily pop either a 40 amp or better yet a 50 amp breaker into your breaker panel and fix the tripping breaker with your existing Lincoln AC-225 welder which would allow you to use it to its full WOT potential.
b) Unfortunately, then you could no longer operate your air compressor without risk of fire because if the compressor were to malfunction then the oversized breaker would not protect the undersized wire so you could no longer safely plug your compressor into the weld receptacle like you are doing now.
c) I am assuming powering the air compressor from an alternate location is not practical nor is running a new service line since you have not upgraded your shop service already. For
improvised safety you could jerry rig a flexible adaptor pigtail that would temporaily plug into the welder receptacle and then run to a small disconect box that contained 20 amp breakers then run to a new receptacle for the compressor. The 20 amp breakers in the adaptor pigtail would protectect the house wiring from fire if the compressor ever mal-functioned. It would not cost much to make this adaptor pigtail ($30 or less ), but it would not technically be NEC compliant either and is in violation of NEC code. That said it would be better than powering of the welder receptacle alone with oversize breaker on undersize wire. Since it is flexible and not hard wired to the house it is easily removed if you sell the house.
If none of this makes sense to you then forget I ever wrote it as electricity kills if you are not very careful and fully understand what you are doing.