You can't cause, because that's a Wizard only-only spell. However, you might be able to do that with a permissive DM or with an appropriate homebrew sorcerous origin. You can also just cast it directly via wish, which you can cast multiple times if you have the right Epic Boon(s).
You almost certainly can't do this. There's no time between casting and the effects happening. You could use Contingency for this (there are ways to have more spell slots around), except Plane Shift is too high of a level. Instead, you need to be friends with, or True Polymorph into, a Metallic Dragon variant spellcaster that knows Plane Shift (for reasons. You can also coerce one into service with Gate+Dominate Monster or whatever), and have your simulacra using twinned wish duplicating simulacrum. Despite the fact that this makes no sense (Wish-duplicated spells shouldn't be twinnable since you aren't casting them), it is legal via Sage Advice Compendium errata stuff:
andAnd so by spending 7 sorcery points your simulacra can duplicate both you and the dragon (or a simulacrum of her), or you and a simulacrum of you.
Sidenote-- — you have infinitely many Xanar in the Material Plane for a bit here, which might be uncomfortable but doesn't have any mechanical penalties and can be dealt with by having the dragons warp sooner if it is a problem for some reason. Next problem:
Other people run the Abyss as only having ℵ0 or some smaller number of points or spaces on each layer. In that case, this might be a larger number than the number of demons. Even so, there's no guarantee that your ℵ0 is the same size as their ℵ0. It might be bigger, smaller, or something else entirely-- — the game does not in any way define the superstructure of the Abyss. Comparing infinities is not easy, that's why ∞ - ∞ is undefined, not 0.
Also, you're rolling initiative and even with infinitely many rolls you won't beat any creature who rolls higher than it is possible for you to roll or who has special abilities allowing it to go first. Any creature who goes before you might take actions to elude your army, for example by casting antimagic field or plane shift or wall of force or meld into stone or doing anything else that negates infinitely many eldritch blasts. And any creature who doesn't go before you still might escape with reactions unless they are surprised (which, admittedly, seems likely, but is still not guaranteed). And those who don't, might, like with antimagic field residents, be immune anyway for some other reason.