Hi J..
Not sure about all of the symptoms that you listed but I can tell you that my daughter cut her teeth EARLY. By the time she was 2.5 months old, she cut TWO TEETH! NOT good news for a first-time mommy trying to breastfeed. I remember bringing her in to her Ped's office and everyone was shocked.
From that point on, my kiddo cut a tooth for each month.
I recall that my daughter had a slight fever each time she came close to cutting her teeth, lots of drooling, but since she was too young for excessive mobility, we didn't see much hand-in-mouth action until she was a little older.
Good luck to you. OUr kiddos sure keep up on our feet, don't they?