I've been to a few countries outside of Europe and the US. Obesity and lesser but unhealthy fatness may not be as widespread yet there, but they're not that far behind. Also, what some cultures consider "not fat" isn't actually "not fat." Plenty consider "chubby" to be perfectly normal (and even attractive).
Of course they are, it's part of the European continent. This is like saying citizens of Lichtenstein or Switzerland or Norway aren't Europeans.
Russia is also technically in Europe but a lot of Westerners don't consider Russians Europeans. So I see no reason why continental Europeans could't consider the British as non-Europeans. In fact, there are plenty of Western Europeans that don't even consider Eastern Europe as 'real' Europe.
Ukraine is in Europe. I don’t know about Russia. I thought Russia spans Europe and Asia.
Russia indeed spans both Europe and Asia but almost all Russians live in the European part and majority of all Russian history and culture happened or is linked to Europe, not Asia. Similarly Turkey technically is also in Europe (small part of Turkish territory) but nobody seriously claims that Turkey is a European country based on this technicality. Another example would be Israel which technically is not in Europe but is considered to be more European than Middle Eastern. So the Brits not being European is not really such an outlandish claim. Especially that there is a growing tendency for 'European' to actually mean 'related to European Union' instead of its original, geographic meaning.