Multiple glyphs of warding can't ward the same thing...
The target of the glyph of warding is listed as object touched or up to 5 sq. ft./level, and the spell's description says
Multiple glyphs cannot be cast on the same area. However, if a cabinet has three different drawers, each can be separately warded.
This prevents chained glyphs exactly as you describe, and for good reason. For example, were multiple glyphs able to ward a lone tiny box, triggering them all simultaneously creates disastrous consequences for the approaching army—seriously, a tiny box will be picked by someone and opened (especially if it's a shiny box), and if there are hundreds of glyphs of warding on that tiny box then boom—goodbye, army. (To actually run such a trick, try the spell explosive runes instead.)
...And a touch spell stored in a glyph of warding will affect the creature that triggers the glyph
The spell's description says
You can store any harmful spell of 3rd level or lower that you know. All level-dependent features of the spell are based on your caster level at the time of casting the glyph. If the spell has a target, it targets the intruder.
Emphasis mine. The spell touch of idiocy has as its target living creature touched, so a living creature triggering a glyph storing touch of idiocy will be the target of the spell despite the spell's typical casting method. (By the way, multiple penalties from multiple touches of idiocy—as they're from the same source—shouldn't stack, but ask the DM; a penalty is a little more complicated than a bonus, despite the lengths of those linked entries.)
Although the text isn't specific, it's safe to assume that summoned creatures from a spell glyph aren't random creatures from the summon monster list and instead chosen by the glyph's creator when the glyph is created. Likewise, a suggestion spell held in glyph should offer a suggestion that the caster chooses upon creating the glyph rather than offering a suggestion of the caster's choosing when the glyph is activated.
That said, this is a really expensive way to secure a wagon
A heavy wagon only costs 100 gp. Spending hundreds of gp to protect it is an unusual use of resources. If available, consider hiring some locals to guard it. They'll be thankful for the generous 1 gp per day that you pay them to guard your wagon.
You scribe the circle and runes when creating the glyph.
Glyph of warding:
Spell Glyph. You can store a prepared spell of
3rd level or lower in the glyph by casting it as part
of creating the glyph.
At Higher Levels. ... If you create a spell glyph, you can store any spell of up to the same level as the slot you use for the glyph of warding.
As you cast the spell, you draw a 10-foot-diameter circle on the ground inscribed with sigils
(PHB, p. 246 and 282, emphases mine).
To put the teleportation circle in the spell glyph, you have to cast it, including drawing the circle and sigils. You can't have them drawn when the glyph is triggered.
Normally I'd say that this kind of use is a stretch, but in this case I'd say it works, for one very critical reason: you, the DM, are on board with this.
In my own game I would rule against it: a glyph on a surface is measured in feet in the spell's description, and regardless of it being vague otherwise, I would feel quite within my responsibility as the arbiter of the game reality to say that something so complex that it's normally measured in feet could not in any way be reduced down to mere fractions of an inch. (At this point I would also point out to the player that if they're determined, they can just research a new spell that does what they want directly instead of trying to press an ill-suited spell into service.)
However, this is your game, not mine, and the same principle applies: you are responsible for arbiting the game reality. And in this case, you are clearly on board with the player's use of the spell. You even have supplied a cooperative NPC dwarf to get around the problems of engineering that took centuries to solve in our own history of firearms!
The only issue seems to be that you have one (or more?) other player who isn't so on board. In this case, since you are willing to grant the use of the spell, your problem is not the spell, it's mollifying the objecting player(s).
To do that, reassure them that the ruling is in the best interest of the game being fun, which is the ultimate goal of play. "The spell is vague on that point. It's obviously not casting it in an object, so the object rules don't seem to apply, just the surface ones. It's a very small surface, but I'm willing to allow it because it's vague enough that it isn't clearly improper, and because the result will be a lot of fun." Modify as appropriate, based on your judgement and your knowledge of your friends.
If that approach doesn't work, there is probably a fresh question to be asked regarding the social situation surrounding this.