It is a good example, because its someone who was never in the US being charged, tried and jailed in the US for an alleged crime against a British company.
Dual criminality means that the act that they are being extradited for is also an offence under UK law. It does NOT mean that they actually broke UK law. And in the case I am thinking of, they were never prosecuted in the UK. Thge UK-US extradition act is also severely lopsided, with a firm case having to be presented to extradite from the US, but only reasonable suspicion being required to extradite from the UK.
You do not appear to understand what a republic or a democracy is, so I'll ignore the last sentence.
"Independent" does not mean unaccountable to the people. The President is independent of Congress, and vice versa, but both are accountable to the people. Well, the current president doesn't seem to think so, but legally he is.
The civil service is not a part of the executive but is a co-equal branch.
You are correct. In principle, presidents have no authority whatsoever to dictate how an agency runs. The executive branch should have zero authority over the civil service, which is intended to constitute a fourth co-equal branch of government.
In the US, in principle, the status of the civil service as co-equal to, and independent of, the executive should be added to the Constitution and enshrined in law for good measure. Not that that would help much with the current SCOTUS, but a Constitutional change might possibly persuade the current government that absolute authoritatian control is not as popular as Trump thinks.
That is the idea that, in Britain, entities like the NHS and the BBC have operated under. Charters specify the responsibilties and duties, and guarantee the funding needed to provide these, but the organisation is (supposed) to carry these out wholly independently of the government of the day.
It actually worked quite well for some time, but has been under increasing pressure and subject to increasing government sabotage over the past 20-25 years.
It's also the idea behind science/engineering research funding bodies the world over. These should direct funding for grant proposals not on political whim or popularity but on the basis of what is actually needed. Again, though, it does get sabotaged a fair bit.
Exactly how you'd mitigate this is unclear, many governments have - after all - the leading talent in manipulation, corruption, and kickbacks. But presumably, strategies can be devised to weaken political influence.
There are two kinds of egotists: 1) Those who admit it 2) The rest of us