I am in the middle of this procedure, being fairly old myself. I can only say, get yourself an appointment at the Deutsche Rentenversicherung a.s.a.p., do not leave it till you are 64 and three quarters. It will take time. You will need to document things such as your higher education (Anrechnungszeiten), for which you need not just a degree certificate but a Bescheinigung from your university of your period of full-time study. As regards employment in other countries, do not contact the relevant agencies there yourself, the Dt Rentenversicherung (penguin, sie heißt BfA seit ewigen jahren nicht mehr!!) will do it on your behalf.
I have had two long appointments with excellent Sachbearbeiterinnen at my local office, one of whom straightened out the mess of a previous less excellent one. Your entitlements from other countries will be sorted out by a special department in Berlin, to whom your file will be sent and your Versicherungsverlauf documented.
I am sure you will be entitled to draw on contributions from more than one EEA (not just EU, apparently) state, though I personally have only UK and D contributions, so I cannot say for certain.
But apparently entitlements to UK pension, I was warned by the Sachbearbeiterin, may be held up until Brexit negotiations are completed. So probably Barnier is the best one to get in touch with on that score, he will know more than anyone else, certainly more than anyone at the Dept of Work and Pensions.