I am a clerk and I would have assigned light bulb liability to you for all bulbs not working that were working when you moved in.
So that is easy, go through the inventory and count up the number of non working bulbs, cross ref with the number at check out... how many do you owe? But as you say, you LL has agreed to remove that charge.
Water staining in a bathroom ceiling can have a number of causes, but often a water source above. So, for example, if there was a header tank that was leaking and you ignore the signs/didn't report them then the LL can ask you to recompense them for part of the damage. But in a flat it is usually a leak from upstairs, so yes, challenge that.
Cleaning... did you pay a professional company? Did you ask for an end of tenancy clean? The usual routine is to get the cleaners back in to complete the job, but, if the landlord can adequately prove you left the flat dirtier than would be expected they can claim - though the arbitration schemes don't like it! Cleaning is the cause of almost 3/4 of all disputes, LLs are routinely disappointed.
All you need do is write back and say you do not agree to the propose deductions. Make an offer, be sensible, that shows you are willing to compromise. Then leave it to them to make a claim with the deposit scheme. If you don't hear from them in 10 days, claim back your money.
Have a look at the website for the scheme you money was protected in... check the date it was protected, it should be less than 30 days after you moved in you should have had the certificate for it too!
Panic not, just follow the procedure!