Your frozen hose is toast. The faucet might be salvageable.

Yes, you can fix a leaky faucet if it’s just a worn washer, but a frozen hose with a split is done.

Hoses are cheap. If water froze inside the hose, the ice expanded and cracked the rubber or vinyl. No tape, patch, or clamp will hold that for more than one use. Just buy a new hose.

For the outdoor faucet (sillcock), turn off the water supply