Should outside hose bib be suppled from shut-off valve with a bleeder port from upstairs bathroom
Drains on the inside valve for outside faucets are indeed normally open for the winter to prevent freezing.
You close them when you turn on the faucet in the spring - evidently you didn't look when you turned the valve on?
Builders are not required to use any particular sort of pipe, so long as it meets code, unless otherwise specified in the contract.
Plastic pipe (especially PEX) is usually preferable for outside faucets, as it's less prone to burst in a freeze event.
Code does not particularly care where your outside faucet is fed from. If you wanted it fed from a different location, that should also have been specified in the contract. If it was not specified, the plumber presumably took whatever path was easiest given access to plumbing to supply water and specified location of the outside faucet.