Clue 1: This station does not feature the word Road, or Street or any other endings like that.
Clarification requested: Do you mean the station name does not have a suffix at all, or just not a road-related one?
A very long shot at Huyton. Served by trains to Liverpool South Parkway (which to my mind is not a "direct service to an airport", so if this is wrong then I should lose a point for an impossible response); hourly services to Manchester Airport pass through non-stop.
East Midlands Parkway is a bit of a punt...
Coleshill is a penalty. All westbound services from there terminate at New Street without going anywhere near International.
I'll throw in a clue 5a
5a) Robinson understood what I was getting at with clue 2 perfectly.
Not East Midlands Parkway.
5) This 2 platform station is served by only one TOC, and in normal operation only has that same TOC passing through.
Corby is single platform, and falls foul of service to two airports - I don't even think it has service to one.
However, Wavertree is the correct answer
Doesn't Corby to London call at Luton airport?
Limited service to Derby via East midlands airpot