It will effect the back pressure the engine is designed for and the O2 sensors won't have a true reading. Just find somebody with a mig welder, disconnect both battery cables, and have the ground clamp as close to the hole as possible, turn the amps way up on the welder, the welding wire is meant for steel you're manifolds are cast iron, I've welded cast with a mig before so I know it does work, because of the heat on the manifolds there's nothing on the shelf to just plug the hole. Or, is the hole small enough to tap it with threads and put a bolt in it? A bit of red loctite will keep the bolt in place

Yes, it will adversely affect performance. And replacement of the header is the only way to fix it unless you know an experienced welder

yes fix while reasonable has cost go up from here. now if you it wield it the best way is find old and bolt it to it because they will warp. I use to clean the area good and preheat it hot and braze it and leave bolted down till its cool and don't use water to cool

yes. the engine is designed to run with a certain amount of back pressure. when this is reduced the valves can burn in time. ultra high performance cars are designed to run with little or no back pressure.

Yes, it has an exhaust leak. It could effect the way the oxygen sensor(s) read as well.

Indeed: Any exhaust leak will effect it.

Will a hole in the header of a Mustang affect the way the car runs? I know it will make it louder. I just need to know if it will affect the performance and how much about it usually is to fix. Thanks in advance!