Things that will make no sense to you, no matter how long you live in Britain

I have no idea what 'property tax' pays for in the US... does it pay for the services I've mentioned?

Well council tax is property tax. The US rationale is that if it is a tax on the property, then the property owner should pay it....after all they own the property. It goes, generally, for the things you mentioned, as well as providing a significant part of the public education budget.

Again, to me,...I think it is a wash.....in the case of a renter, one could argue that a portion of the rent goes towards the property tax anyhow...

But given that the property owner of the rented unit is generally the one with the higher financial resources, the US system gives a more progressive feel (rich guy paying more).

Regarding water bills, in the areas of the US I am familiar with, even if it is a municipal system, use and billing is generally separate from property tax - so regardless of the depth or frequency of the bath, the landlord isn't responsible for payment.

It goes, generally, for the things you mentioned, as well as providing a significant part of the public education budget.

Oh yeah, council tax pays for schools as well... being blissfully child-free, that one didn't immediately come to mind.

"And the whole "upward chain" thing, where apparently, people don't have to actually sell you their house that is for sale if they can't find another house to move in before your sale is completed? What's up with that?!"

This is also an English thing, in Scotland you agree the house sale, the lawyers exchange letters and that is it the price and moving in date are agreed at that point, the only way to get out of it is if the property searches find something wrong that wasn't disclosed.  Pulling out for any other reason leaves you liable for the other sides expenses - so if the buyer pulls out the least they can expect to pay is a relisting fee, readvertising for as long as it takes to sell and other costs the lawyers add. 

Housebuying in Scotland is easier, no chains, prices are usually advertised as offers over by a certain date, and lawyers are also estate agents.  When I bought my house the lawyer threw in a free will.

I've lived in the UK all my life and I don't get cricket either.  I once got taken to Lords though and its great - there are bars and restaurant and museums - unless you glance over a the pitch you hardly ever see the game, I was there for 5 hours and saw about 10 minutes actual cricket.

and lawyers are also estate agents.  When I bought my house the lawyer threw in a free will.

Buyer: Is that asbestos up there? It looks like asbestos...
Lawyer/estate agent: Oh don't worry about that. Can I interest you in a free will?