Plumbing line seems to have air in line. Our neighbor is having an addition done on their home. We have done nothing to our plumbing, we now experience an extremely loud reverberating pulsing when we turn on our hose faucet outside, which reverberates through the house, into the fridge water line, and in the walls. We also have a problem with a toilet after this has happened where it will not refill once flushed unless we turn the faucet under the tank off and back on.

What may have caused this and how do we fix it?

Not your neighbors fault. In a pressurized water system there is no such thing as air trapped in the line.

You either have trash trapped in the hose bib or you have a loose washer.

Turn water to the house off.
Remove the stem of the hose bib. Check the washer screw to insure that is is tight. I would just replace the washer at this time. Turn the water on briefly to flush out any debris that might be caught in the hose bib. Reinstall the stem.

Sounds like a loose washer in the toilet stop valve. If it is a compression fit, and it probably is, just replace it while you have the water to the house turned off.