Yes. For instance, you can chill a glass that you are going to use for a cold beverage.
Warning: A closed glass container can explode and spread shattered glass all over the inside of your freezer if it is too full. Liquids expand when they freeze, and if there isn't enough room for them to expand inside the container, they will burst out of it.
This can happen with other containers, too, but you won't see the wreckage that you get when it happens with glass. It's the kind of mistake you don't make more than once.
Yes, but it is likely to crack if you fill it up with liquid and then seal it.
NEVER stack two or more glasses in the freezer. Stacked glasses act just like a closed glass container when placed in the freezer and will break, even when there is nothing in them.