whoever buys the airport will be passing on the cost of the purchase to the airlines and their passengers so fees might not come down as you hope.
No, they most likely will not immediately but in time they may well do. BAA did say however that there would be instant cost savings and management costs would fall when they admitted Stansted could be run for £5 million cheaper per year after the sale so there is the potential for landing fees to come down.
The new manemgemt and increased competition for Stansted is enough stimulate interest and potential growth from airlines very quickly though by itself. Even for the low-cost carriers, the lowest landing fees is not everything. Whatever happens, Ryanair is committed to Stansted and the fact is, they will work very hard with the new owners and as they say "Stansted's managment can't get much worse" so things will be looking up in the next few months/years whichever way you look at it. I very much doubt a new ownership will make things even worse than they currently are!