ICE starts 5 seconds after backing up - normal ?

All three of those things can happen. If the display shows it sending charge to the battery, that's probably what it's doing.

When it pumps air for the resistance of it, that's to hold your car speed down, as can happen when you're going down a hill and the battery has too much charge to accept regen braking, or you have shifted to B.

MG2's RPM is always locked to one ratio to the wheels, so there's never a risk of MG2 overrevving without the car going crazy fast (> 100 MPH).

MG1 can overrev at lower car speeds, depending on the engine RPM, so sometimes the engine runs to prevent that. It isn't used as a high-resistance air pump then, but just to sort of loaf around at the needed RPM, neither adding nor subtracting more torque than necessary.

In general, unless you really want to delve into details and become obsessive over it, "just enjoy driving your car" is really pretty good advice. It has a lot of different things it does for different reasons, and it knows all those reasons so you don't have to, and it really all works pretty well.

If the car gets old enough, it probably will eventually tell you that the battery's worn out, and it will likely be right, and there are choices for crossing that bridge when it comes. I've seen efforts to try to estimate "remaining battery life" and predict when that moment's going to come, but I'm not sure how well they really work.

 

all 3 of mine did, and our hybrid camrys as well. can't get all the way out of the garage without the engine starting, and they were all purchased new.

 

It is very possible a 2008 could have a "rebuilt" cheap (mix and match used modules) replacement hv battery already - but a few 2008s are still original. If someone did use a "rebuilt" those batteries often get weak in a year of less. A new oem set of modules easily last 10-15 years.

An obd2 reader won't tell you much even if you buy the upgraded Dr Prius app. Even a Toyota Techstream scanner is not definitive on a car without codes. Most cheap scanners can't even read hybrid codes although the Dr Prius app can read hybrid battery codes.

While not totally relevant, reverse is only electric propulsion.

The Ice engine has to warm up anytime it is cold regardless of hv battery state.

A good battery and a warmed engine can stay off during a traffic light; a worn battery may not have much capacity left and quickly discharges. Capacity is different from voltage; voltage can be high but discharges fast; that is a worn battery. It does not means replacement is imminent especially without battery codes.

No hybrid battery codes yet? Just drive it daily and save your money in a repair fund.