Bruxing is when a rat grinds their front teeth together. They can do this both when relaxed or when they are stressed. You may hear them doing this or feel it if you are petting them.
Boggling refers to when a rats eyes seem to pop in and out of the sockets. They can do this when bruxing. It can be a little disconcerting the fist time it is witnessed, but is generally a sign of contentment.
Squeaking is a normal rat vocalization that can happen in a number of situations. You may hear your rats squeak while playing, fighting, or when you pick them up if they are fearful. You can hear some examples of rats squeaking here.
Rats have poor eyesight. When you see them exhibiting this behavior they are usually trying to judge the distance to something. It is often more noticeable in pink-eyed rats as their eyesight is poorer than their dark-eyed counterparts.
Most rats like to urinate on things. Since their eyesight is poor, they rely more heavily on scent when communicating or exploring their environment. Male rats typically will scent mark more often than female rats. You can read more about this behavior here.
This is a normal behavior, especially among young rats. This activity helps to prepare them for finding their place in the social hierarchy as they get older. You may hear them squeaking while play fighting, but they shouldn't be screaming. This behavior should not be discouraged unless it appears to be escalating to the point of injury.
Even if you make sure your rats have access to food at all times, you will still probably find stashes in hidden spots in their cage. This is a natural behavior carried over from when they were still wild and didn't know when their next meal might come.
These are just a few of the most common rat behaviors typically seen by owners. A much more comprehensive list can be seen here.