Are these two hose connections correct and also what part is this?

Can't tell you about the hoses; it's been way too long since I've worked on a Neon, but the broken part you're referring to looks to me like the rubber boot that's supposed to be covering the constant velocity joint. If you go online or to an auto parts store and ask for a CV Joint boot for the front left wheel, that should get you the part you need.

Couple of notes here, though; you said it was the right, driver's side, both of which can't be correct. Whenever you refer to right or left on a car in reference to parts, it's always from the perspective of sitting in the driver's seat, so the left front wheel will be the one on the driver's side, and the right front wheel will be the one on the passenger side.

Secondly, chances are pretty good you'll need to specify whether it's the inner or outer boot. Most CV axles come with two boots; one that installs in the transmission (the inner boot), and one that connects to the wheel itself (the outer boot). So you'll need to specify which one it is in order to be sure of getting the right part.

Good luck, hope that information helps!