I'm from the UK, and as other postes have said, it is definitely Foy-ay, Buff-ay, Val-ay.
I woulod only ever use foyer in relation to a public building - most typically a theatre, but possibly also a large hotel as well. In a rivate house I would refer to the Hall or front hall.
In the North, 'yard' is used as well as garden. I lived in Manchester for many years and my (2-up/2-down coronation st terrace) had a yard - it was fully paved, with a gate to the back ginnel. I know a lot of people who would still use 'yard' even if they were living in properties which had gardens rather than a yard.
I think that 'garden' is the most common usage , however, and is used for any enclosed outdoor space whcih belongs to a particular home, whether it has grass, plants, hard surface or a combination. (the exception would be if you just have a driveway to park a car on, in which case you'd be likely to call it a drive, not a garden.
Having one parent from either side of the North/Side divide and having lived both in Manchester and in Somerset, I am inconsistent in my pronunciatio of things such as Bath etc.