I'll let the pros handle most of this but here is a little help... A shop compressor is probably a poor choice for several reasons. At 125 psi that is way more than you need. Water pressure developed at something like .45 ish psi per foot of depth, so at 10 feet deep you only need 5 psi to overcome the water pressure to be able to move the air. A shop compressed is also probably not designed to run for extremely long periods of time and will likely burn out or break quickly and often. Not to mention it probably cost a lot to run all day. A compressor for aeration needs to be low maintenance, highly energy efficient, and fairly low pressure by comparison to a shop compressor. An aeration system will be great for the cold winter because it can keep a section of your pond from freezing over.
Buried PVC is ok for your aeration system but it makes for an aeration system that is going to be hard to service if a problem arises. If you use weighted line then you just drop it in and if it ever n needs to be pulled up it is easy. You won't be able to do that if you have buried PVC and unburied PVC will float.