Bad Starter??

I have a 97 Contour GL 2.0. For a while now when the car is being started it has been making this loud grinding type sound. Now that its getting colder the car is having a lot of trouble starting up in the mornings. During the afternoon when its a little bit warmer it starts up but while in park idle it stalls out after a few seconds. After that it wont restart.

I'm pretty sure its the starter but I'm not a professional or anything so I would like someone to help me out here.

If a starter is bad would it cause the car to stall out?