Welcome to the boards.

Change the oil asap as the unburnt fuel will have slipped past the rings and into the oil.

With that said also do a compression check and see what that looks like.

If the person doing the welding grounded the welder to the frame and then welded on the exhaust that is mounted with rubber isolators and bolted to the engine with rusty bolts, the only reliable return path would be through the O2 sensor and the ECU.

The battery connected "can" help reduce voltage spikes when welding is preformed on cars but the welder needs to make sure that they have a true solid ground close the where they are working. If you disconnect the negative cable it is a good idea to jumper it to the positive terminal to prevent the main line from just floating.