I have to change the waterpump on a Diahatsu Sirion 1.3 2007 model. Are there any hidden problems I might encounter, or is there any special attention I need to know about? Any special tools needed?

Blockage in the exhaust is quite likely a cause.

something not replaced correctly check all fluids for level and for cross contamination --pressure test coolant and oil systems --check all sensors and wiring --timing

indicates a failing/ dry clutch throw out bearing
change you habits and place the car in neutral at lights with the foot of the clutch
That will get you a bit of extra time before repairs are required

possible failure of the flex bit of the exhaust
you will have to take it to an accredited exhaust specialist shop to get a quote on the repair

Blocked Fuel Filter, Bad fuel Pump or Blocked Exhaust

these are where I would start.

There should be no reason to 'adjust' the timing belt: it is either fitted and working or not fitted..therefore having to replace one? If you do have to replace one, it is not a job for the faint hearted! You will also have to make sure you have a spare car for back-up.. e.g: if you plan to do this job and get driving in short time think again... You need as much room, both visual and physical around the plastic timing cover, you need to ensure the timing cogs are pre marked (with dots) showing what is called TDC (top dead centre) ENSURE THESE DOTS LINE UP PERFECTLY BEFORE REMOVAL AND AFTER RE-FITTING NEW BELT.. apart from that crucial bit.. it's simply a matter of cleanliness and patience.. remember to loosen the belt tensioner prior and re-tighten after fitting new belt.. DO NOT OVER TIGHTEN!

drive belt side is one

if the transmission has a dipstick similar to the engine dipstick you fill it through that tube using a small funnel or the like.....hope this helps.....cheers.