Licking & Tail Chewing Behaviour

[ell&diesel]

Have searched for a smiliar thread but nothing comes up that is relevant to this problem so here we go...

Trooper (10 month old Amstaff) has been with us for a week; now that she's more settled & comfortable with us, some of her "quirks" are making themselves quite clear. One of them is this strange behaviour with her tail. She doesn't chase it but when she gets excited she will all of a sudden drop to the ground and chew and lick the end of it. I don't have a camera atm so can't show you a photo, but the tip of her tail is hairless, scabby & dry. Some other threads suggested a product that vets use to make bandages taste bad, so I'm going to pick some up on the weekend, because she simply won't stop chewing it. Once she starts you have to physically remove her tail from her mouth and begin some kind of activity that distracts her - then, when she enjoys the activity and gets excited, she tries to eat her tail again. Is this a learned behaviour do you think, or a semi-OCD thing?

Also, not sure if I'm just being paranoid, but she licks thing. A LOT. During "quiet time" (before she goes to bed), I tell her to get into her bed and then spend a few moments just patting her. When I do this she will try to grab my hand in her mouth (extremely gently), put it in front of her and then lick it endlessly. Last night I tried to see how long she'd do it and after a good seven minutes of licking every inch of my hand and wrist, she wouldn't stop. When I pull my hand away she follows it, grabs it, and licks it. She also licks glass (windows in the car; glass back door) every few minutes when she can.

On top of this, she has a complete freak-out if myself or OH walk away from her. She is fine during the day for a few hours while both of us are at work - she hasn't dug any holes, torn any washing, or barked excessively - but if we go to the supermarket and one of us gets out of the car to buy something from the shops (with the other one in the car with Trooper), she launches a full-scale assault on the car trying to get out - chewing the windows, digging at the doors and generally panicking. In the house, if one of us leaves the room, she HAS to follow us. If we both leave the room at the same time, she tears around like a lunatic until she can find us both.

I'm guessing the third behaviour is a kind of insecurity-related thing where she doesn't want to be left alone; but that doesn't fit with her being perfectly fine at home by herself at times. The licking me & licking the glass is just odd. Any ideas on why she might be doing these things & suggestions on how to get her to stop?