The second part, the frequency, correct. The first part, incorrect. The US and UK systems are quite different. In the US the transformer secondary winding is centre-tapped, giving 120-0-120V. Connecting to one live (hot) conductor and the neutral gives 120V. Connection to the two live conductors gives 240V
In the British system the distribution system is almost always three phase. The transformer is normally in a local substation, serving a much larger area than the small pole mounted ones common in the US. The secondary windings are connected in star (wye), with the neutral conductor connected to the central point which is earthed (grounded). Until recently the nominal Voltages were 415V between live conductors, and 240V between any single live conductor and neutral. In both cases +/- 6%. A few years ago this was changed to 400/230V +10/-6%. Nothing really changed, except on paper, it was to standardise the Voltage in Britain (415/240V) with that in the rest of Europe (380/220V) We should now refer to it as 400/230V, but most people still call it 415/240V; it is usually closer to the latter figure.
Domestic installations are normally single phase. Each house will be fed one of the three live conductors, and the neutral. Typically each phase will be used in every third house along a street, i.e. if you are on the red phase your neighbour on one side will be on yellow, while that on the other side will be on blue. The earth and neutral conductors are always different, but, at least at the substation, the neutral will be at earth potential, and should be very close to it elsewhere. There is no second live conductor, no centre tap on the transformer, and no 120V anywhere. The only place in Britain, but not in the rest of Europe, that you will find a centre-tapped system like in the US is on building sites, and a few other places such as stations on the London Underground, where portable tools ure used on a 110V system which is centre-tapped to earth (55-0-55V) which is fed from a local isolating transformer. Note that this can only be used for 110V equipment; connecting to just one side to get 55V is not permitted.
Correct in the US, quite different in the UK. Our plugs have three pins, live, neutral and earth. Except for a special one used on shavers and toothbrushes we have no two pin plugs now; we did in the past, but they have not been made for many decades. You will not find a plug with two live pins here. We do have both 4 and 5 pin plugs for industrial use. These have three live and one earth pin. The 5 pin ones also have a neutral pin. We do not have normal mains plugs with two live pins.
For most equipment the frequency difference will not matter.
European flexible cables are colour coded:-
Brown - Live Blue - Neutral Green and yellow striped - Earth
The colours can be different for British equipment more than about 30 years old, and the situation becomes complicated with installed cabling in buildings, and all types of three phase cables, due to changes which have taken place in the past, and further changes which are taking place now, to harmonise colours throughout Europe. If you have to deal with anything like this consult an electrician who is familiar with European standards.
British mains plugs have the earth pin, the large one, at the top. when looking into a socket the live pin is on the right, and the neutral pin on the left. Of course, when looking onto the pins of the plug this will be reversed, as you are looking in the opposite direction.
European equipment which has a three core cable should not be connected to a 2 pin American socket, nor should the earth conductor ever be connected to either the live or neutral conductors. You should never find European equipment where earth and neutral are conected internally, nor where the neutral is connected to the case (unless the equipment has a serious fault, in which case it should not be used anyway) Assuming that it is connected corrected correctly, European 220/230/240V equipment should operate from a US 240V supply, with the live conductor connected to one 'hot' leg, and the neutral conductor to the other. A possible complication is that European equipment will be likely to have single pole switches and circuit breakers which when tripped would leave what is normally the neutral conductor, but which in the US would be connected to one of the 'hot' legs connected, and therefore live at 120V. What US electrical regulations would have to say about this I've no idea.