In reverse order.....
2) Given that everything ordered will have a Postcode, the onus is on the seller to collect the relevant tax and pass it onto the relevant authority. Impossible to police completely, I know, but even if someone chose to live their purchasing life completely online, the majority would be from 'legit' companies such as Tesco so even though that occasional motherboard from Japan will slip through the net, I think a high proportion of the tax will be collected.
1) Harder - In my opinion, second homes that are left empty in small villages are a huge problem anyway. Every empty home is a home that is not using the local school, the local shop, the local pub, the local Post Office etc., and contributing to them shutting down. Not to mention driving up local house prices and pricing people with no home out of the market, so I would like to get rid of them anyway, or at least should attract a 200% council tax rate, rather than 25%, to make up for the damage they do to the local economy. I guess it would need studying as to how much revenue could be collected in local purchase tax and exactly how widespread the problem of 2nd home owners really is, before deciding how to factor this is in i.e. Just because I believe they are a big problem, doesn't mean they really are...