Definitely pick up the Visa - that'll push you up to 16 pts/$ (using rough 2-to-1 exchange rate), assuming you get the card before your stay. You'll be Silver from the get-go, not that it really matters a whole lot at FI.

The whole "base rate" stuff means no points on incidentals at FI - not really a huge issue as you can't really do much incidental volume at an FI anyway. Candy bars? Sodas? I think that's about it. (Do any of them charge for WiFi?)

They should post Premium Pounds as a credit, thus you'd earn points and pay taxes on the full base rate of the stay. Sometimes they goof and post it as an adjustment - which means you earn points and pay taxes on a lower amount. In most places, this is roughly a wash - I don't bug them about it because it simply causes more confusion at check-out. The Premium Pounds itself will likely confuse them. I've actually had to explain the concept of foreign currency to front desk clerks in the past.