Providing trains run to time, then a 30 min frequency between Knaresborough and York is already possible despite the single line. Currently in the daytime there are two an hour from Leeds to Knaresborough and return, one of which terminates/starts there - this could fit in the gap as in the below example (extra train in bold):
KNA 10.15 10.45 11.15
CTL 10.23 10.53 11.23
HMM 10.27 10.57 11.27
POP 10.35 11.05 11.35
YRK 10.46 11.16 11.46
YRK 10.11 10.41 11.11
POP 10.16 10.46 11.16
HMM 10.24 10.54 11.24
CTL 10.27 10.57 11.27
KNA 10.35 11.05 11.35
The issue is probably more that it puts the line up to full capacity and doesn't allow for any contingency, charters etc (a bit like the TPE route with its 6 trains per hour!). Also, whether there is a path from Skelton is an issue. So in my mind, capacity around York and unreliability are probably just as much a problem as the single line. Back in the 1980s, it was suggested that Harrogate line trains could avoid crossing the Skelton bottleneck by them using the freight line and then round the (now removed) curve where the ROC is to a new platform adjacent to platform 16 (as was). Clearly that isn't possible now!
With regard to the station for Leeds Bradford Airport, the idea of a new station served by existing trains is ill-thought out. They are already busy without airport travellers and would slow down services even further - as deltic08 points out, the trains already take longer now than they did years back (largely due to the opening of Burley Park & Hornbeam Park). Having checked the 1979 timetable, it was 34 mins Harrogate-Leeds back then. If they want to go down the road of a station with a bus shuttle for the mile to the airport, a far better concept in my mind would be to build a siding next to the existing line, and operate a separate dedicated Leeds-LBA Parkway service every 30 mins (perhaps calling Horsforth only, thereby giving it a service every 15 mins).