What happens if nobody participates in a giveaway?

The Entries will come, no worries there. The closer it gets to ending the more you will get. Not many enter at first when there is a day or more left on the running time.

Some of my giveaways were simmilar to yours and the restrictions were way higher and I got anywhere from 15 - 63 entries. The "open" giveaways got 90 - 153 so yeah. You should be golden :)

Does that affect public giveaways as well?

No, in public giveaways you'll get CV even if you only get 1 entry.

It just gets cancelled and you can simply create a new one, the five participant rule applies only to invite-/group-only or region-locked
GA's - public GA's are already valid at one entry and thus will grant you the according CV.

From my knowledge, region free public giveaways will always give you CV. Not sure about region locked ones, though.

If a GA ends with no entries you can do whatever you want with the key and create another GA, if you feel like it.

So, what would happen if nobody participates and the giveaway ends? Simply no winner, make new one with the same key?

Yes. Maybe lower requirements or increase the duration for the second run.

Also, I've read that invite-only need at least 5 participants to count towards your contribution. Does that affect public giveaways as well?

It's in the FAQ (Contributor Value and Levels, What is contributor value?, article 2):

If a giveaway is invite only, region restricted, or limited to a whitelist or Steam group, it will only add contributor value if it receives 5 or more entries.

Public GAs aren't mentioned, since this rule doesn't affect them. They only need one entry.