Not valid Heathrow Express
Not valid London Underground, Tramlink, London Buses or Docklands Light Railway
Valid on Elizabeth Line (was valid on Heathrow Connect that ran same service previously)
Valid on London Overground
Elizabeth Line and London Overground are both National Rail services and all route appropriate NR tickets are valid on these. Unfortunately it is not unheard of that some staff are poorly trained and give problems with unusual tickets, any suggestion that Interrail is not valid is 100% incorrect.
Not sure about the validation, there is a staffed ticket office at Heathrow T2/3, If they cannot validate it is perfectly acceptable to travel with the unvalidated pass to your next station, Paddington presumably, where you can get it validated.
On the using pass+ oyster or contactless. There is nothing wrong with this but do be careful. There are a number of locations where it is possible to transfer between National Rail and other London services without passing a barrier or validator so it can be easy to inadvertently travel without a valid ticket if you are not careful. At some stations it may require exiting the gateline with pass and tapping in with oyster or the other way round. Always remember to close out an oyster/contactless journey, while changing directly to a NR journey using your pass would be valid if you don’t tap out at the end of your oyster use you will be charged extra for having an incomplete trip.