How do I save a picture from a message? This is the menu I get for holding it

If it's an image, tap, hold and then tap Save to save it to Photos.

If it's a sticker sent as a message, open Photos in Split View or Slide Over, tap, hold and drag to Photos.

Use Multitasking on your iPad

From Use Multitasking on your iPad:

Use two apps at the same time with Split View

With Split View, you can use two apps at the same time. For example, you can view photos while you compose an email. Or look at a location in Maps while you search for vacation ideas in Safari.

How to use Split View:

1. Open an app.
2. Swipe up from the bottom of the screen to open the Dock.
3. On the Dock, touch and hold the second app that you want to open, then drag it off the dock to the left or right edge of the screen.

How to adjust Split View:

• To give the apps equal space on the screen, drag the app divider to the center of the screen.
• To turn a Split View into a Slide Over, swipe down from the top of the app.
• To close Split View, drag the app divider over the app that you want to close.

You can use Split View with iPad Pro, iPad (5th generation and later), iPad Air 2 and later, or iPad mini 4 and later.