PhysX is just the physics library, like Havoc, used within the game and doesn't automatically require the use of an NVIDIA GPU. NVIDIA allow for more complex PhysX acceleration on their cards, but are by no means required. PhysX can be used on any CPU, even consoles.
The sudden drops in frame-rates could be momentary blips of run-away physics calculations, or it could be the result of an inefficient rendering engine (as is often the case with these types of ports). I should point out that I ran the game on minimum PhysX details too and it made no difference to the spikes (they happened regardless).
The game was run with everything maxed and at 1920x1200 resolution... but the game only renders up to 1080p (again, the sign of a console port), hence the black borders in the screenshots (they were put there by the game, not by me).
The use of the controller will help even out the demand put on your left hand for all major controls. There isn't anything stopping you from programming your mouse for weapon switch with R or the Caps-Lock and tab targeting. If you're comfortable with a controller, then by all means use it.
I do love the art and style of the game, it's what kept me going. It really livens up towards the end (as well as some of the story), it's just the actual 'game' part nearly drove me insane... ironically.
