If I buy Android gift cards in America, will I be able to redeem from Europe regularly or via VPN? Also, will I be able to download movies via VPN or proxy from the US play store?

No idea, but you can get them in the likes of Tesco too.
Though in stores I have only seen the £50 ones so far.

It might have even been in Sainsburys but they were right next to the iTunes cards somewhere or other.

They sell them at Tesco and Morrisons. I have purchased a couple nof £10 gift cards myself.
The Google play website says that you cannot use US gift cards outside the US. Same for any new other country that the gift cards are available

Fair enough with US/UK - but doesn't that breach european guidelines if you can't use a French card, for example, in the UK?

No. Why would it?

Are Euros required to be accepted in the UK? Is Sterling required to be accepted in the Euro zone?

Would it be possible to use a UK gift card in Ireland or even a French one?