Yes the battery should be covered (at least they were when i was working )
but they will likely want to put it through a full charge and test before getting approval from Vx

 

I don't know, I'd double check with vaux.
Although I have my s/s battery covered for free with RAC breakdown cover, offered to me as a free upgrade, which I took. Think it only costs something like an extra £11 per year on top of my usual home start premium. Which in my opinion would be well worth taking. As they usually stock the batteries and fit at the road side, during the event of a failure. As we know s/s batteries are not cheap, hassle taking your car to the dealers, as they usually charge anywhere from £60-£120 to look, then we'll go from their sir!