Whats the best wall and repair glue?

I'm not sure what you are making the wall with - rocks, pavers? I found this article that might help - https://www.hunker.com/13424887/how-to-build-a-river-rock-wall-with-mortar

Any Quality Mortar will more endure the elements than Gorilla Glue. I Imagine you would need 3 gallons of $3 an ounce Glue if you go that route.

Your mortar will cost less than $1 a pound. On a wall you can do alot with:

mortar+Concrete colorant to match

However how great was that fall of Humpty's wall?

Is a good question...

You may be better off just Picking up Pieces and Pulverizing the Stones as an aggregate for topping to make new bricks with concrete and sprinkle the brick powder on top.

How big,heavy is Humpty Dumpty & his wall?? What is the wall made of, is it inside house or outside, is it toy or life size? All this will determine best glue to use. E6000,Gorilla Glue,JBWeld. Stacked walls don't need anything to hold them if they are done right-Dry Stacked. That's how most Ancient cultures built their worlds.I'm guessing since you asked you are not a Mason so yes you'll need something to hold them in place. Use the E6000, unless it's an actual wall outside then yes to mortar

Is it a dry stack wall? If so you need a really really good old time stone mason, not many around these days.

A dry stacked wall is staggered back as layers rise. There is usually a great deal of 2B gravel behind the wall area, a sloping ground trench with sleeved drainage pipe over more gravel. Over 4' high wall should be done by a professional, as permit is usually required.

The wall is good, Humpty not so much. He cracks me up sometimes