Can I safely put a pipe wrench on an outside faucet and on the pipe it is attached to and turn it one quarter turn to the side so the hose connected to it won't be bent and spray at the attachment?

NO!

Outside spigots are soldered directly to your water supply pipes. They attach about 1 ft. past the wall. If you try to bend the spigot, you will be twisting the copper tube and stressing the solder joint. To fix the potential mess, you might end up tearing down a wall and replacing the unit.

Please do not do that. As for the spray, make sure that the washer is inside the hose. If there isn't one, go to the hardware store and get one.

Not likely. You could only do that if hose bib is a threaded pipe fitting. That's only likely if you have galvanized water pipes. More likely that you have copper pipes and the hose bib will be sweat soldered. If it is a regular hose bib or sill cock you may be able to heat and reposition it. It may however be a frost proof one and the connection to the piping is at the interior side of the wall.

I agree with Harold, check your Bib the type is threaded or sweat type, if you can post a picture will be more help full, Thanks.

Regards,
John

There are two types of hose bibs. Sweat and threaded. If your hose bib's soldered on then forget it, but wait! You don't necessarily have to have older galvanized pipes to have a threaded hose bib. We stubbed out with a copper threaded male adapter that a FIP hose bib threads into. We installed them this way in case the homeowner ever had to replace them. If you have a threaded hose bib it's safe to give it a 1/4 turn to pick up the hose. Good luck, Tom

You can also purchase "no kink" hose bib. Its threaded part is under different angle so it there is no pressure on hose.

Please click on the link below it may gave an idea that what type hose bib you got, like Tom and Milo says there are 2 types swaet and threade, Thanks.
Regards,
John

Brass U.S. Made Hosebibbs from PlumbingWorld.com