<<Can LHR atc see what you dial in the alt preselect window via mode S?>>
Yes.
<<you have a level segment>>
...from LAM until due north of LHR because the departures climb to 6000 beneath lowest useable FL. The CDA (3nm/1000 feet) to 09s will commence once clear of the SIDs and will approximate between 25 to 30nm. Unless Number 2 Director is a god there will be a short fly-level before GP intercept. (Unless things have changed since I did it, some time ago now...)
Some of the distances to touchdown used to be 'persuasive' to achieve a desired response, so yes, there was an element of artistic licence. Radar....or RADA? Dramatic Art to achieve a desired effect....