MapPilot Pro Android Mobile App Free Trial

What menu items are missing? 

There are a number of things that are not currently added to the Android version. 

https://support.dronesmadeeasy.com/hc/en-us/articles/8216315538196-Current-Limitations

The Terrain Awareness panel is showing all the time in the left side of the bottom. You do not need to be connected to the aircraft but you do need to have a valid flight plan designed in order to use it. 

See the video here:

https://support.dronesmadeeasy.com/hc/en-us/articles/211810943-Terrain-Awareness

I don't actually care for the items listed under Current Limitations, though I can see how they'd make life a little easier.

After choosing New Mission, my only options are Normal, Grid, and Linear. Choosing Sampling or Spot displays a dialog saying they are not available.

AHA, I found it!
It is available from an unlabelled icon (a slide-up tab) at the bottom of the screen. I was expecting it to be up on the main menu, labelled Terrain Awareness (as seen in videos of iOS I guess) - my bad. I recognised the icon after watching the video you linked.

Thanks!

We are glad to hear you were able to figure it out.

"After choosing New Mission, my only options are Normal, Grid, and Linear. Choosing Sampling or Spot displays a dialog saying they are not available."

Those items are listed on the Current Limitations but are primarily intended for use in precision agriculture with very specific equipment.