If you can fit it through the opening, you can put it in there.
This would effectively make your Bag of Holding a wonderful trap/container for your Genasi.
As for opening it from the inside, rules do not state you can or can not. Lots of people have asked this before, but I personally do not feel that you can open the bag from an extra planar space because you aren't technically inside a bag, you're actually on a different plane. To me, that means you can't manipulate the opening of the bag.
But that's my opinion on it.
The Rules Don't Say.
I never like giving one of these answers, but the simple answer is: it doesn't say one way or the other, anywhere.
D&D 1st Edition is where we first saw the Bag of Holding introduced, the description given is...
As with other magic bags, this one appears to be a common cloth sack about 2' x 4' size. The bag of holding opens into a non-dimensional space and its inside is larger than its outside dimensions. Regardless of what is put into this item, the bag of holding always weighs a fixed amount. This weight, the bag's weight limit in contents, and its volume content are dependent upon its quality as shown below.
[Snip table]
If overloaded, or sharp objects are placed within so as to pierce it, the bag will rupture and be ruined, and the contents will be lost forever in the vortices of nilspace.
AD&D is much the same, but added the rules of what happens if the bag is pierced from the outside, and what happens if you mix bags of holding and portable holes.
D&D 3E added rules for the sort of Actions required to retrieve stuff from the bag, what happens if you turn it inside out, and what happens if you stuff a living creature into the bag.
4E Nerfed the daylights out of the Bag of Holding, but added no new rules or flavor.
5E rolled things back to closer to 3E rules, but without multiple 'qualities' or 'sizes' of Bags of Holding.
And that brings us up to date. The fluff text on a Bag of Holding has not changed since D&D 1st Edition. At no point has the interior of a Bag of Holding, or how it appears when being filled or emptied been laid out. Even branching out to Pathfinder, they simply lifted the description straight from 3E and left it alone.
What I would do...
My personal ruling that I use in my games, which has never really caused trouble...is that the bag appears roughly as full as it actually is. If 50% of its capacity is full, the bag appears 50% full. If it's empty, it looks empty. This has never really come up in terms of putting the Bag inside of something else...but has always been an easy way for characters in-game to tell how full the Bag is at a glance.
(For extra fluff, I've also always ruled that the inside of a bag of holding looks....like the inside of a bag would. Just really big.)
Best Answer
The Bag would be destroyed.
The item description states:
In this case, the bag would almost certainly become overloaded. It would rupture - and would be destroyed. The creature would be placed somewhere on the Astral Plane. The amount of damage, if any, is unspecified and would be up to the DM.