Can I delete a photo a guest uploaded?

Yes: as the host you can delete any upload from the gallery, with the trash icon on the photo, from the full-size view, or several at once with Select, and it disappears for every guest at once.

Your browser is recognized as the host's when you created the event in it or opened the host link from your confirmation email; on another phone, tap Download all on the event page: it asks Are you the host? and emails a code to the host address; enter it and that phone is recognized as the host's, trash icons included.

Deleting is permanent and removes the file from the gallery and from any ZIP you request afterwards; a ZIP already emailed to you is unaffected. Guests can delete their own uploads too, but only their own; you are the only one who can remove someone else's.

There is no approval step: uploads appear in the shared gallery as soon as they arrive, and everyone with the code sees them. If you want a quieter gallery, keep the PIN on so only invited guests get in, and look through the gallery during the evening.