Display photos from iPad on TV without Internet connection

Here's one way...

If your TV supports HDMI then use a Lightning Digital AV Adapter.

Use the Lightning Digital AV Adapter with your iPhone, iPad, or iPod with Lightning connector. The Lightning Digital AV Adapter supports mirroring of what is displayed on your device screen — including apps, presentations, websites, slideshows, and more — to your HDMI-equipped TV, display, projector, or other compatible display in up to 1080p HD.

It also outputs video content — movies, TV shows, captured video — to your big screen in up to 1080p HD. Simply attach the Lightning Digital AV Adapter to the Lightning connector on your device and then to your TV or projector via an HDMI cable (sold separately).

You also need a HDMI Cable.

Another possible way is to use a Lightning to VGA Adapter.

Use the Lightning to VGA Adapter with your iPhone, iPad, or iPod with Lightning connector. The Lightning to VGA Adapter supports mirroring of what is displayed on your device screen — including apps, presentations, websites, slideshows, and more — to your VGA-equipped TV, display, projector, or other compatible display in up to 1080p HD.

It also outputs video content — movies, TV shows, captured video — to your big screen in up to 1080p HD. Simply attach your Lightning to VGA Adapter to the Lightning connector on your device and then to your TV or projector via a VGA cable (sold separately).

You also need a VGA Cable.

Yes you can share content without an active internet connection. Once you have your Apple TV and your iOS device signed into iCloud and AirPlay works - you can disconnect both from the network and they will work ad-hoc to make a bluetooth/WiFi connection to stream content (sound and images) from the iPad to the Apple TV.

Whether you just disconnect the router and there is a local network - that will also be used for AirPlay - but an internet connection is only needed to arrange the initial account sign in one time.

Have a look at: Use AirPlay to wirelessly stream content from your iPhone, iPad, or iPod touch

https://support.apple.com/en-us/HT204289

With AirPlay, you can stream music, photos, and videos to your Apple TV, or stream music to your AirPort Express or AirPlay-enabled speakers. And with AirPlay Mirroring, you can display your iOS screen on your Apple TV.

Pay specific attention to the peer-to-peer AirPlay section of the above article.