I don't know about the UK, but if you hold dual citizenship in Germany (German+X), you have to present your German ID when you enter the country.
Correct (for Germany) - although this is only a fairly new requirement.
For the US, it's mandatory to enter (and technically, leave) using your US passport.
For the UK, it's NOT mandatory to use your UK/EU passport - however if you enter using (say) a US passport then you are entering as a visitor, and must meet the requirements of your entry, such as leaving within the X days you are given.
Personally I'd suggest using a UK/EU passport if you have one, if only because the lines are generally much shorter, and very much faster!