You cannot keep your other citizenships if you naturalize in the US. You have to renounce them.
Of course, DHS and DoS almost never check, so this is hardly ever enforced. However, if you're employed in certain fields (politics, legal, etc.), it's highly advisable to play by the book.
That's not true. The US allows dual citizenship, there is no requirement to renounce. Other countries may not allow dual citizenship, but certainly between the UK and the US dual citizenship is perfectly allowed and quite common.