I have a few doubts - can you help me, please?

[Claudia (Italy)]

1) to wave a flag OVER or ABOVE one's head? are they both correct?
2) a commission IS discussing or ARE discussing a problem?
3) can I write "river Thames" or do I have to use the capital letter also for "river"?
4) London's "big wheel" or "Big Wheel"? I found it in a dictation, and I didn't use the capital letter because I thought that it wasn't the name of the wheel (isn't it called London Eye?!)
thank you very much in advance,
Claudia

[Tdol]

1- Both could be used.
2- In American English, the singular is generally preferred, but in British English the singular and plural are both used.
3- Use a capital.
4- I would say 'big wheel' because it isn't the name.