Drawing

Not at all. In most of these the drawing is a physics input rather than artwork - a shape that has to work, not one that has to look good. Guess My Sketch is the exception, since somebody has to recognise it.

You draw the shape of your character's legs, and they move using exactly that shape. Different terrain wants different shapes, so redrawing mid-level is part of the game rather than a sign you got it wrong.

Both appear here. Routing games like Park Me: Draw Path are puzzles you solve, while the physics-driven ones are closer to skill games where the same idea can work or fail on execution.

Often, yes. Drawing with a finger is more natural than dragging a mouse, so a phone or tablet tends to give you finer control over the shapes than a desktop does.

Yes, every one of them plays free in your browser with no download and no account needed before your first sketch, whether you're using a mouse or a touchscreen.