Yes, the core features (Timer, Ambience, basic Quest Log) are completely free to use.
Yes! Once loaded, the timer and tasks work locally. However, you need internet access to stream the high-quality ambience sounds.
You gain XP for every task you complete. Leveling up is purely cosmetic right now, but it tracks your consistency over time.
Currently, we use a standard Pomodoro-style 25-minute focus block. Customization is coming in v2.1.