Differences details, signature, licence number are all that should be required for confirmation of differences training.
There is however a recommendation in LASORS for a refresher if you've not used differences training within 2 years. It would be prudent to have done so - an insurer may otherwise regard you as not having been sufficiently professional in the approach to your flying.
For an FAA derivative licence, the locals seem perfectly happy in my experience to have the UK/JAA system explained to them, and so long as you're qualified at home, they are content that you are qualified in the USA.
VFR on top is permitted in UK airspace. However, it may not be permitted on your licence. A UK issued "vanilla" JAR PPL or CPL holder cannot fly VFR on top, but an IMC or IR holder can.
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