Can I wear my night guard after tooth extraction or will it crak with grinding?

Yes you can. You are not likely to crack it. It should not be a prob at all but it wouldn't hurt to ask your dentist.
Yes. The night guard is very important for protection. The extraction may cause the guard to be looser. If that is the case we suggest having the guard relined at the dental office. This will enhance the retention or the tightness of the guard following the extraction if needed.
Ask your dentist. Cracking the mouthpiece would probably not be an issue, but if the night guard needs to be modified, have the dentist do it, not yourself. I would ask about wearing it or not for the short term.