newbie question

Welcome!
Part one - yes
Part two - no
But if almost /nearly dead / mortally wounded (versus 'completely' dead) , it'll still run. Once it gets really bad it'll most likely throw a code & then you can get a 'no cost' replacement pack, at least while under warranty.
.

 

What he said.
Two entirely different questions.

 

no need to plug in, or worry about the hybrid battery, haven't had any issues yet, and you still have warranty left.

 

Lots and lots of misconceptions about the Plug in Prius, but you're close. Here's another way to say pretty much what the others said.
You have one dinky little 12V battery to run the computers. That's the small one. If it dies, your car won't go because the computers won't run.

You have one gigando 4.4 kWh battery to run the electric motors. That's the big one If it dies, your car won't go.

If you don't plug in that 4.4 kWh battery, you'll just be using the bottom portion of its possible state of charge and it will run just like a regular Prius, enabling you to take trips longer than 10-12 miles.

 

Yes, it's a fully functioning Hybrid...Toyota actually had commercials that touted the "option" of plugging it in or not. It will function as a "regular" Prius if you do not plug it in.

No, it's a Hybrid, designed to work in Synergy with the ICE, The Battery, and Electric Motors. If the Hybrid Battery dies, it will not switch over to being a fully functioning ICE vehicle.