Various questions

It's very conservative. From my experience, when the last gas gauge bar starts to flash, the "distance to empty" is already reading 0. But the reality is that you have around 2.9 gallons left in the tank or about 120-150 miles of driving left before running out of gas.

Kind of shooting in the dark with this, but if one of aforementioned modes malfunctions, the ECM would throw an error code.

 

In PWR, very short distances off idle produce large throttle openings.
Normal has a more linear pedal travel to throttle opening through the range.
Besides requiring more pedal travel to open the throttle off idle, ECO also reduces the A/C compressor power.

All fully open the throttle if it is pressed to the floor.

So these modes are mostly just different software maps relating pedal travel to throttle position, they are unlikely to fail individually.

 

There is significant safety margin built into the fuel gauge, as a part of 'customer expectation management'. Fuel consumption varies enormously depending on the immediate circumstances, based on things that the car cannot possibly predict, and that most drivers cannot be expected to fully understand and keep track of. Without that safety margin, many drivers would be running out of fuel in situations where the car earlier indicated that it had sufficient fuel range.

For more details about actual fuel range vs the displays, read the very first post of this thread:
[WARNING] Running out of gas (Gen III) | PriusChat

You missed one mode, Normal, which is what you get when all the other modes are turned off. Eco, Normal, and PWR differ primarily in how the gas pedal is mapped to the actual throttle response. I.e. it is mostly a user interface change, giving it a different 'look and feel', not a real change to the engine/propulsion system. There isn't much of anything that can go wrong that relates to just a single mode, not the others.

EV is different, but is not something you ever really need to use. While useful in some situations, it also opens up plenty of opportunity for drivers to sabotage their overall MPG through improper use.