Welcome @CyberZed404
Can I presume that you’ve already found the end-point - APIs: Details - Transport for London - API - and been able to execute things like
https://api.tfl.gov.uk/Journey/JourneyResults/940GZZLUHSD/to/940GZZLUMED
(you will need your key at some point but it will generally work for you without until you get rate-limited!)
The time it takes… is simples

The “All stops on the chosen route” isn’t part of what you get out of here. However, you can cross-ref the data with the likes of
https://api.tfl.gov.uk/Line/central/Route/sequence/inbound
https://api.tfl.gov.uk/Line/central/Route/sequence/outbound
to get the list of stops and their orders.
What line(s) the train(s) use on the selected route…
There are two types of line on the London system… most of the lines are stand-alone and run only their own trains: Bakerloo, Central,
And there are others that share tracks such as the Piccadilly/Metropolitan (Rayners Lane->Uxbridge), Metropolitan/Chiltern Trains (Hertfordshire), Circle/Met/H&C/District (Zone 1).
You can tell they are “sharing metals” as they use the same platform numbers.
Sometimes there are times when this looks like it might be happening but ISN’T such as the parallel running of the Bakerloo and Northern Lines between Waterloo and Embankment.

See Clive's UndergrounD Line Guides and Detailled London transport map (track, depot, ...) for help with this.
https://api-portal.tfl.gov.uk/ is the reference for the current TfL apis.