Informally, it's sometimes referred to as "vat", e.g. calling a tax inspector "the vat man".
If used in context, no one is going to get confused by either pronunciation though.
I just realised that I have no idea how I normally pronounce VAT... It's like trying not to think about pink elephants.
Yes.
We do, but every now and then someone will pronounce it as 'vat rhymes with fat', so it's also understood. On the TV it's almost always pronounced as an acronym.