You'd be able to keep the chassis, but all of the wiring and such would need replacing to be able to work in the Digital World since home tech doesn't work here. And yes, you did read the rest correctly.

Venusmon would have likely mentioned the storage feature, so it shouldn't be that much of a surprise. If you character missed it, someone else could have mentioned it. It's all in how you wish to play it.

For your standard-sized backpack, well pack, we'll say it takes up two spaces. For something more akin to a military or hiking backpack, three or four would be standard for it being packed to full capacity. Weight plays a big factor in how much space it takes up.