Let me start with "gear mode". There are 3 "power source" modes in the Clarity. I'm using Honda's terms from page 14 of the 2019 manual:
1) Electric (EV) -- electric motor driving the wheels, with the electricity coming solely from the battery.
2) Hybrid -- electric motor driving the wheels, with the electricity coming from the battery and/or the engine (used as a generator). This is almost always the mode that you get when you accelerate hard, hear angry or busy bees depending on your perspective, etc. I strongly believe this is the mode you're talking about, and recommend you just call it Hybrid, engine running, EV off, or anything, but not "gear mode" because that's confusing people.
3) Engine -- engine is coupled directly to the wheels. This is what people here call "gear mode" (because it's "indicated by the gear icon" per the manual). This only happens at certain higher speed ranges under steady highway speeds. When coupled like this, there's only one gear ratio, so you'd never get particularly high revs in this mode (unless you were driving 150 MPH, which A. isn't possible in this car, and B. probably wouldn't result in gear mode anyway
Important not to confuse "Hybrid" here with the "HV" switch where you ask the car to try to hold a charge level (which will result in a mix of all of the above driving modes).
Now, to some of the other points:
- You mention the power meter turning all white -- I'm pretty sure that happens any time the engine is running; it doesn't mean the car thinks the battery is depleted. You only get a blue portion of the bar when you're actually back in EV mode. If the engine stays running for whatever reason (because it hasn't warmed up yet, because it's anticipating another hill, etc), the bar will stay all white until the engine actually shuts off. I'll double check this later today.
- Note that 5 bars is really just 3 bars to EV-range-0, which occurs at 2 (sometimes 3) bars. Again, no idea if there are different algorithms for anticipating loads/hills when the charge is at higher or lower levels within the "EV remaining" range. A battery at a low state of charge may well not be able to generate the same peak power, so while for normal driving the battery might be treated as "empty" at 2 bars only, under heavy repeated loads it might do so at 3-4-5. Remember that the battery system in the Clarity can't provide all of the instantaneous current the motor can use even at high charge; that's why the engine has to kick on to add on a boost under heavy acceleration.
Honestly, the burning smell is the main thing I'd be concerned about and have them check for oil leaks or other issues. The other behavior really doesn't sound unexpected for the kind of driving you were doing. The Clarity is not an SUV with a smooth V-8 powering it up any hill, nor is it a Tesla with a huge high battery pack silently zipping up those same hills. But it doesn't pretend to be either of those; it's a hybrid with enough electric oomph to handle 99% of driving, and a "lawnmower" engine that can be pushed hard to handle the rest. And it's quite a bit cheaper than either of those