Getting water to external spigot
Toilets are typically supplied using 1/2" pipe, while it's common to use 3/4" to supply a spigot. You can certainly tee off the toilet supply and feed a spigot, though you might not quite get the flow you're expecting.  Should be fine for watering flowers, vegetables, etc. Though may come up short if you're trying to water the lawn with a sprinkler. You'll also probably notice a pressure drop off, if somebody flushes the toilet.

If you end up supplying a spigot (however you do it), I'd recommend installing a new anti-siphon frost proof sillcock. The one that's there looks like it's seen better days.