Each country has their own way or ranking their military personnel. Originally, the United States' ranking system was based on the way the British ranked their military, but over the years, it has changed.
The services use different insignia for different ranks. A double silver bar in the army is a captain. In the Navy and the Coast Guard that same insignia is a Lt. Go to www.military.com and they may show you the different insignias.
The officer ranks are both the same. However the enlisted ranks are different. The Army also has Warrant Officers where as the Air Force does not.
The US has been the most powerful military nation since WW2 (1945).
riveters. they could work in factories, but were not permitted to serve in the military.
No such thing in the US. Nor UK.
Although there are different types of military badges for the US Army, there are no subdivisions for military insignia. The total number of military insignia for the US Army is 57.
All services have ranks that have different names. The enlisted tier starts with E-1 and goes through E-9. When you first go in you are and E-1 and as you progress through the ranks and get promoted you go to E-2, E-3, etc.
UK finance is different from US finance because they have different policies regarding financial matters. They also use a different currency so it can be very different.
That depends on what sort of company you had in mind. An aviation company will have several, as most helicopter pilots are WOs. An infantry company will have none, as there are no WO positions within the infantry CMF. Note that this applies only to the US military - British and Commonwealth militaries will differ, as their Warrant Officers ranks are the equivalent of Senior NCO ranks in the US military.
The battery for US and UK is the same but the different is the battery charger You should get a UK charger for you battery.
The sea traditions of our British counterparts and that of many other Navies of the world.
In the way of actual paperwork, none apart from the marriage license. The UK citizen comes in on a visa waiver and you can get married in the US. For the US citizen to get to the UK, that is where the paperwork comes in. You both need to go to the UK embassy in the US and apply for a marriage visa for the US citizen to come into the UK. The US spouse will then be able to work straight away when you get to the UK also based on that visa.