They had to raise the level of the site before building the runway in the first place so I'm sure they could fill some ditches if required for latest regs. There's also space to extend the runway.
A tram link wouldn't have to terminate at the airport, it could continue to the Advanced Manufacturing Park (currently woefully served by public transport or cycle paths), Catcliffe (further housing developments also under way) and perhaps a decent Park and Ride facility to get M1 drivers out of their cars and into the city centre quickly and easily. The existing tram network is not at capacity so these services could supplement rather than replace those to Meadowhall.
The HS2 station for South Yorkshire may well end up at Tinsley Yard so the opportunity is there for a fantastic 'Sheffield Parkway' setup with business flights, high speed rail, light rail and motorway connection.