You can book a taxi via following methods:
Online: http://www.wythenshawecars.com/
Telephone: +44 161 436 4000
Yes, it's possible to pre-book a taxi with Wythenshawe Cars, please contact the company.
Wythenshawe Cars has both regular and air-conditioned taxis, please mention your preference at the time of booking.
Please contact the company on their helpline number to make any changes.
Generally drivers will meet the passengers at the arrivals on airport pick ups but do check with the company.