How do you empty / dispose of the sealed bags between replacing cartridges?

You can dispose of it by putting it in the garbage bag, tie the garbage bag up, and throw it in the trash. It's ok to throw it in the garbage just like you throw away used diapers.

How do you buy more cartridges and what is the cost of the cartridge?

The Dry flush cartridges come in a pack of 3. It is $84. You can find it here: https://www.shoptinyhouses.com/collections/dry-flush/products/dry-flush-refill-cartridges-3-pack

Is the plug in USB? Will I also get info. as to where to purchase extra cartridges

It does not the plug is just a standard 12 volt wall plug. 

There's also an option to use solar: https://www.shoptinyhouses.com/products/dry-flush-portable-solar-charger
Or charge it via car charger: https://www.shoptinyhouses.com/products/dry-flush-portable-cable-car-charger

Here's a way from extra cartridges: https://www.shoptinyhouses.com/products/dry-flush-refill-cartridges-3-pack

For space savings and the safety and convenience, I’m wanting a “Wet Shower”. Can this toilet be left in the shower to sit on during the shower when the shower water is running?

The Laveo Dry flush is water resistant but not water proof. The toilet must be covered with a trash bag or some ssuitable waterproof cover when used in a wet area.