Is the incidence of home invasions higher in UK or US?

Different definitions of assault. Many forms of assault in the US are counted as misdemeanors. Every credible site will point out the difficulty of comparing the two between each country and the difficulty of comparing statistics in the US where each state has different definitions of assault as well, and different standards of reporting these to the FBI or other federal agencies.

Not according to UN comparisons - same rate in both countries - but then they at least make an effort to use comparable authoritative sources.

See above. If you are going to use a source, at least use one that's credible. Even then this is within reporting errors.

Not true. The UK law states that anyone can use any reasonable force to defend themselves and their property. This does not include disproportionate retribution after the event, but in retaliation to a violent attack you are quite within your rights to use any weapon you have to hand to disable your attacker.

So the Police overreacted and they were not charged. The issue is not the law it's the Police on the case at the time.

One example proves nothing. How many people accidentally shot by the Police in the US?

What a meaningless post.

--
The process of observation changes that which is observed, hence you cannot photograph reality.