A Common Modelling Scenario That Got Me Stumped

For REQ1 you could add any fields you wanted to display into the fact table, e.g. Arrival Name, Dest Name, Arrival Code, Dest Code.

For filtering the measures you could have a single, disconnected, airports table and create a calculation group with a calculation item like

Airport Filter =
VAR SelectedAirports =
    VALUES ( Airports[Code] )
VAR Result =
    CALCULATE (
        SELECTEDMEASURE (),
        KEEPFILTERS ( 'Fact'[Arrival Code]
            IN SelectedAirports
                || 'Fact'[Destination Code] IN SelectedAirports )
    )
RETURN
    Result

Use this as a filter on any visuals where you want that behaviour, or potentially as a report level filter if you want it  everywhere.