I can't actually believe you are asking all these questions whilst spouting forth thousands of words on the solution to the London capacity problem/BA and VS strategy. Bizarre.
How many 777-300ERs will BA operate after these orders?
Presumably 15 considering they have 6 now, are due in receipt of 6 further direct from Boeing as well as the 3 to be leased from ALC. However, these aircraft were originally ordered to bridge the gap following delays in 787 delivery so it will be hard to know how long they will stay.
Will they replace any of their 747-400s?
That was the purpose of the A380 and 787-8/9 orders.
When the leases expire, will they order A350-1000s?
As above; these aircraft were (at least originally) meant to just bridge a gap until deliveries of new aircraft are such that they can be returned to the lessor. But our guesses are as good as anybody's as to whether they might take the A350 - has been previously discussed and we can only speculate.
When are they due to order more 787s and A380s? (I know its been delayed by the takeover of BMI)
I'd presume that this will take place after those aircraft have begun to arrive in the fleet. Certainly the 787 will have to prove itself as a viable type following recent problems experienced by other operators. But once again, we'll have to wait and see.
When will they withdraw the 737-400s
An announcement on 737 replacement is due this year. The rest of the fleet (as well as airports like JER) would indicate that an A319neo/A320neo order might be prudent as their replacement. Depending on when the first aircraft arrive, they could start to go from 2015 onwards.
When will they order the A319neo/A320neo/A321neo?
Some of the EF/SFG aircraft are ageing - an neo order might be the most sensible replacement. This could be in two years time; maybe more - there is currently no pressing need to replace most of the current generation of aircraft.
By the way, I'm considerably younger than you so probably shouldn't have to be answering questions like this. Perhaps you might consider learning something about the industry before writing the essays which you do?