Braking is regenerative and will go a bit to charging the battery. There are also flappy paddles behind the steering wheel, that set certain levels of regenerative braking when you take your foot off the go peddle.
You can change the eco meter to rev counter in the settings. It’s highly unlikely the engine will come on if battery % is sufficient during a hill climb.
1) As GG but, less often than when heating.
2) Any smart plug will have to handle a sustained 10A over a prolonged period and you’d have to pay particular attention the plug inc smart plug and socket doesn’t run hot initially. The app allows you to set charging times.
3) There is a maimum of 7.2kW charging, which will take about 2hrs. Unless you are anywhere you can plug in for free or at current electricity rates, I wouldn’t bother.
4) Voltage drop is a reduction of voltage at the end of a circuit and does not amount to using more electricity, as electricity is measured in kWh not voltage (for ease of understanding).
10A granny charger are typically 1.5mm 3 core H07 variety rubber cable which is highly flexible. Each conductor has a cross sectional area of 1.5mm2, in open air layed across the floor it can carry more than double the 10 Amps you are charging at, therefore VD is unlikey to be a problem.