AFAIK you will always need to re-clear Security when arriving from the USA and continuing to a destination within the EU.

Depending on whether or not you have bags to check you may be able to transit airside at LHR, which means no Immigration (which I presume is what you really mean when you say "Customs").

If you are transiting through FRA things are different because Germany is in the Schengen zone (the UK is not) so you are clearing Schengen Immigration at FRA.

Can't help with the ARN baggage question but I'm sure somebody can.