Higher the charging speed and temperature, lower the battery life. Even the quick charge doesn't charge at very high level so difference is not huge, but it still exists.
First sounds like USB 3 problem.
Use Win 7 and USB 2.0 port.
Install MiFlash first, it installs all drivers. After "fasboot devices" return serial number you can unlock.
At least here in Finland warranty covers only devices bought inside EU and only if manufacturer has official importer in Finland and same device is sold here. AFAIK Xiaomi does not have official importer here yet, local Xiaomi resellers warranty covers only devices bought from them.
Not sure if it has stopped completely, but try Clear data from Power app (Settings/Installed apps/All apps).
Edit: Did not help.
Edit2: Enabled Gaming mode and gave it permissions when it asked, might have helped.
Shortest route might be just to flash factory image to it with MiFlash (use Clean all option), this makes it 100% official state.
Stable MIUI 10 factory image is not yet available(?), need to use MIUI 9 and upgrade OTA or use developer version...
MiFlash installs all drivers, but you might need to install it with Win 10 driver signature check disabled.