Nicki
In carrying out your risk assessment it is important to be clear who is at risk and from where the fire risk will arise. Otherwise the investment you make in risk control measures may not give you best value for money.
This sounds like a small building that has been extended. Unless a fire in the either part could not possibly affect the other part (compartment wall to roof level, with no interconnecting doors or shared escape routes) you should extend the fire alarm to the old part of the school as a priority.
The fire alarm for the old part may not need automatic detection unless there is potential for a fire to start and develop unseen- for example would the upper classroom be occupied whilst the ones beneath were empty, or would people be at risk in the upper floor if a fire were to break out in the upper floor store room?
What is the fire separation between the ground floor rooms and the first floor?
After all people are the best form of smoke detection. Probably the person at greatest risk may be the person working in the top floor store room especially if the lower floors are unoccupied.
Otherwise a manually operated fire alarm may be all that you need.
Similarly with fire resisting doors- if a fire occurred downstairs could the escape route from upstairs be affected? If for example there are doors or windows beneath the external staircase? If the answer is yes, then these doors/ windows may need to be protected.
Is there a need for a fire door to the store room? This could perhaps protect people in the class room a little should a fire occur in the store but only if walls are to a similar fire resisting standard. But if someone is working in the store and a fire breaks out elsewhere a fire door on the store will do nothing for them.
The HMSO fire safety guides give advice on this and all other aspects, and the design and advice on fire safety in schools is covered by a special government publication - Building Bulletin 7 has been in force for many years and has recently been superceded by building bulletin 100.(BB100) If you cant find a copy on the internet, then try technical indexes or barbour- your library should be able to help. Its important to have a benchmark standard against which to measure your premises, and then from which to compare the strengths of your building- such as very small travel distances to reach an exit with potential weaknesses such as a lack of fire doors
Hope this has been some help to you.