From your home screen double click your home button. The screen will slide up. Press and hold the photos app till it shakes and the x appears. Click the x. Hit your home button. Click on the photos app. If that doesn't work try a hard reset.
No you won't. When you are in the task manager as shown in this pic
It won't delete from your phone. Just stops the app from running (essentially). If you are in a situation to delete an app it will ask you of you are sure you want to delete the app and it's data. You also can't delete native (stock) apps like the photo album.
A hard reset is accomplished by holding the home and power button at the same time. Ignore the slide to power off. Continue holding both buttons until you see the Apple symbol. Release the buttons. Wait about a minute and your phone will be back to being able to use. This fixes a lot of common problems.