Robbery Games

Bob the Robber 3. It teaches the guard patterns and lockpicking clearly before the later entries start assuming you already know how the stealth works.

Loosely, and not in a way that matters. Each is self-contained with its own setting, so you can start anywhere without missing anything you'd need to understand the levels.

Mostly, yes. The core loop is avoiding detection while working through a building, which makes them stealth puzzles rather than action games - being spotted usually restarts the section.

Bump Bandit. It drops the careful pacing for something more immediate, so it suits you if patient guard-watching is not what you came for.

Yes, all of them run free in your browser with nothing to install and no account needed before you start, including every entry in the Bob the Robber series.