Has a cat ever suddenly jumped out and screeched at you while you looked around the house after you thought you heard a serial killer?

no, ive never had a cat but ive thought about getting one

No but it happened in a creepy, scary building. It's a long story, especially the bit about why the building was scary, but my legs were still running when my body stopped at the back wall.

No, but I'm not sure what a serial killer prowling around my house would sound like. Probably a loud crash followed by muffled swearing from tripping over or barking shins on the clutter. Probably not like a cat, but you never know these days...

I try to be tidy, Didge! I trip over things myself :-)

Yes, there have been cases like that in the UK, though not as far as I know, with double or counter-claims. The Police and Courts do now take the attack on the intruder in defence of self or property more seriously, although with quite clear limits. You cannot go beyond what would be considered necessary and reasonable to fight the burglar off or evict him from the premises, such as chasing him down the street and bashing him over the head with some weapon. I think though the burglar would have a hard time trying to sue a victim who'd simply struck him in response to an assault, in self-defence, and pushed him out the door.

I don't know the legal status here of a burglar who trips over something and injures himself, but I'd have thought it weak unless the court feels that the hazard was a deliberate trap for intruders. It is illegal to set physical traps, but not illegal to have a cluttered home! Most personal-injury claims even at civil-case level in the UK fail. Some result in insurance settlements, but it was interesting and welcome to see that of the rash of "ambulance chasers" who appeared in the 1980s and 90s, thanks to the Government of the day misguidedly allowing "no-win-no-fee" solicitors, most went out of business fairly quickly. The cases were thrown out of court, dropped on legal advice before even going to court, or settled by insurers.  Those still trading probably make a very careful assessment of the case, and only take it on if statute and precedent suggest possible success for them. Oh, and some for the client - I hate to think how much the plaintiff loses from the compensation, in fees. Many of the supposed law firms who advertise no-win-no-fee services are actually only agents for the solicitors themselves, so rake off a second layer of fees. 

The burglar on business premises might have a stronger case if the hazard rightfully should not have existed on health & safety grounds, even though those grounds are to protect legitimate staff and customers. Even then I think the court would have more sympathy with the victim than the defendant. There have been the odd cases where the Police have followed trails of blood-spots from burglary to burglar, but I don't think the burglar was compensated for cutting himself on the window he'd smashed!

"No" ... my freezer door doesn't open from the inside.