I got these last week for my birthday and I'm not sure why they are looking smooshed?

There are several types of violas, some stand up, some are a crawling vining type. What temps are you having now? They are fond of cool temps, have they been watered?

Looks like they need to be watered

It's been outside and got a lot of rain water a day or 2 ago. Should I water everyday? Temps have been in the 50's, down to 40's high 30's at night.

No, not every day, maybe give them more sun- mine survived the cold temps last of Feb. See instead if they perk up later. If you have fresh rainwater, use it to water with instead of tap water. (or melted snow)

Looking at the container, it looks like there are a lot of plants, sometimes its so dense that its difficult to get the moisture to the roots. If its lack of water it should perk up within a few hours, stick your finger into the soil and see if it feels dry. When I see them starting to bend over, its usually a sign they need to be watered.

Update: I watered yesterday morning and they also got a lot of rain last night. They're perking up:)!

I agree with RJ. There are a lot of plants packed in there. If it continues to be a problem, you might want to try to water from the bottom by putting it in a larger pot or bucket of water and let it soak up. Then take it out or it will rot.

Falling rain will almost never penetrate the entire rootball of a container packed with plants. Your plants will still need almost daily watering, especially in warmer weather.

Are the roots all mingled together or can I separate the plants and repot?

Better off doing as LorettaNJ said, also remove the dead flowers

It's not worth separating the roots now. Violas will look good for just a couple of months most of the time. Sometimes you can get lucky.