What does the baby dropping feel like?

It sounds like you might be having some braxton hicks contractions--they're what happens before the real contractions occur. When the baby drops, you'll feel like you no longer have much of a bladder and you'll feel pressure really down low in your belly and pressing into your legs (which sounds kind of like the last part there.) You'll find it harder to walk normally because of the goofy sensations--the baby can take its time dropping.