Fallback server

[#1]

Unlike mail, there is no facility in DNS to have alternate Web servers.
Hence why my Penguin goes walkabout occasionally 
To cover server fall-back you could set up a local server to redirect request to when your main server goes off-line. Something along the lines of a Linksys NSLU2 running NSLU2-Linux. With some trick scripts to redirect web requests, automatically when the main server goes down.
But this will not cover connection issues.
Chilly

[#2]

As stated above this can only be done in hardware -  BUT there is a major flaw...
The problem you have is you can only put it on your line in front of your web server and if your line is down it won't help the situation as connections will never get to it to be redirected to the backup.
The solution has to have access to both main and backup webservers i.e. between the internet and PlusNet!!!
It would only really work if you had 2 web servers on your line so it can switch from main to backup should the main fail but there is nothing you can do if your broadband fails.

[#3]

There are failover providers, like this one Obviously you have to move your DNS to them. I use the DNS service, not the failover, then point the A records back to PN web hosting servers. In your case your A records will be to you own server and the failover A records to PN servers. Their movie tutorial is worth watching.