How long does it take for Apple to fix an iPhone cracked screen?

You only get free repair with the regular warranty if it can be demonstrated this was a manufacture fault. In many cases it is a broken screen due to accidental damage in which case without Applecare you pay the full repair price.

iPhone Repair - Screen Damage [and links to other iPhone repair services] - https://support.apple.com/iphone/repair/screen-damage - includes pricing (note, third party AASP may set their own prices).

The time will also depend upon the damage. I have never had to have this done but I think I read if it is a simple replacement it may take a few hours if they have time to do it that day. However, it could be more than just screen damage in which case they may need to replace the entire unit with a refurbished phone and that will depend upon availability. The best thing to do is call the place to which you wish to take it or set up an appointment online.

By "under warranty" are you referring to the one-year Apple warranty or under an AppleCare+ plan or both? Depending on which of these your phone is under, the cost of the repair could potentially be free, but only the Apple Technician can provide you with a cost estimate based on what they find. This estimate should be free.

Yes, that is the standard warranty and the conditions are as I already described. Broken screens are not normally covered unless it is a manufacture fault (which is rare).