Seal gap between bathtub faucet and cracking tile
That is too large of a gap to seal with caulk. If you are looking for a (very) temporary solution you would be better off with plumber's putty. Get a tub of putty (it is not expensive) and knead it well until it is warm and soft, then pack the void with it. It should do a fair job of keeping the water out for awhile, until a proper repair can be completed.
Proper repair would be removing the tub spout and properly sizing the pipe so the spout was close to the tile, then caulk.