Yes on the internet wirelessly in your suite - I have found connection problematical on the two cruises I have taken with my iPad along. Sometimes OK, often not. And it drops out very frequently. Often it depends where you are on the ship.
No on the photos - you can load them in to the ipad with a special adapter/card reader, that I'm sure Regent does not provide. They won't have editing apps loaded in and you can't download any apps yourself - you would need the master password for that. Even IF they did have editing software on it the only way out is to sync your photos with your computer, upload them to a storage site (again this would need an app), or email them out.
You can manage your photos fine if you OWN the iPad, but their loaner is just for casual stuff like surfing the web and email. You will want to bring your computer too if photos are a priority.