What business challenges does British Airways currently face as an organisation?

Competition from a diverse range of sources:

high speed trains, growing no. of budget airlines, business class only airlines, keeping enough of its feeder flights (and regional operations active) in to London to sustain its long haul operations, staff discontent on widely varying contracts, amalgamating services from gatwick and heathrow into the heathrow terminal 5.

Plus offending business customers by allowing economy class customers to disembark first, due to the new layout of many of their planes - economy seats in front of club. This annoys me!

Just a few of the things I'd be bothered about.

someone wants their homework done for them ;-)

They haven't any trains.

People want a SUBWAY in there airports

this sounds like questions for a BA interview.
Might I suggest looking at www.ba.com to find your answers out.
I work for BA and the two questions you have put are typical interview questions. Might I also suggest you find out about "the BA way" and future plans and goals it will give you the answers that you are looking for.