When a woman is excited, blood flows to her genitalia making them swell (clitoris, vagina, both sets of lips- majora dna minora). They become extremely sensitive to touch so walking, crossing your legs and other motions can cause pleasurable sensations or even discomfort. I suppose this sensation could be comparable to a male erection.
Yes, it is pretty normal. You only see the tip of your clitoris. The rest is underneath your labia (the bulbs) and it can get quite swollen up to the point where it can make your vulva open up like a blooming flower.
You also get wet because this swelling up will squeeze blood plasma from the cells in your vagina's lining. Added to that it gets very hot because of all the blood rushing there.
When you are unaroused, your vagina folds flat on top of itself like a fire hose on a fire truck. It looks like an H with the | on each side and the - between them. It is just the way your muscles in your pelvic floor will squeeze it. It also explains why a doctor will put a speculum in flat before turning it during a vaginal exam. He/she sticks it down the - part and then turn it so that the blades stretch the | | parts apart. When you get aroused, it will turn into an O shaped tube.