Random photos in my Photo album

The level of access someone may have to a jailbroken phone is quite hard to outright measure, but at the end of the day they may be able to SSH into the device (a form of remote access performed over command line), bit then again jail breaking does not bypass all of apple’s very advanced security, so again, unfortunately very hard to say. If it was jailbroken, the chance of vulnerabilities is just much higher so to speak.

Get the big stuff out of the way first. The pictures are not appearing because your device was refurbished and creating a new iCloud account is unnecessary. Plus, you've changed the password. You can also enable two-factor authentication for extra measure.

If you're as closed off as you indicate, someone would need physical access to your phone to add the images. So, the most logical explanation is that the images are coming from you. Open Photos, navigate to the image, and "get info." Those are likely just accidental saves or screenshots.

Jailbreaking is a way to hack an apple device, such as an iPhone, to allow it to be customised and bypass most of apple’s restrictions. If used Incorrectly it can post a security threat. You can easily tell if your phone is jailbroken if you have an app called “Cydia” installed, it will be a non-removable app (like settings for example).

Did you purchase the device refurbished from Apple? If not, there is a possibility that it was jailbroken (people like to set up their phone to bypass Apple's software to load their own or other apps). If you got the device from Apple, and it's been in your possession, it's not an issue. The images don't have any info on them as far as camera used, etc. so they weren't taken by your device or anyone else's. That means they are likely images from the web. I'm still going with accidental save. I wouldn't worry about it too much. If you permanently deleted the images, not much more to do there. If it happens again, I'd take it to an Apple Store and show them.

I would agree; there’s only a finite amount of ways that this can happen. Personally to me it sounds like someone ( a friend probably) is trying to freak you out for fun. Apple has very tight security on their devices, the chance for someone to hack into it (unless you are jailbroken) is extremely low, and even if they did, I’m sure they wouldn’t go to all that effort just to add a few pictures to your album.

Are you certain you had your airdrop turned off too?

Good point. Forgot about that one.

In that case, are you possibly jailbroken? This could add potential security vulnerabilities to your device.

You've pretty much walled yourself off and you don't see Cydia or anything else weird on it as far as apps. I think you're fine. If it happens again, I'd make an appointment at an Apple Store.