Can't say I ever checked mpg on the Z3, easier on my Z4 as its displayed on the dash. Like all cars a lot will depend how its driven, heavy right foot and you pay the price at the petrol pump, steady cruising and it will be much better.
As to your tyres you can determin the age of them from the codes on them, detils here
Does the age of a tyre affect its performance? Find out how to tell the age of a tyre and whether age affects performance.
www.blackcircles.com
Well worth having the tracking checked when you renew them.
Do you have any service history with the car, front suspension and roll bar bushes are worth checking although any issues should have been found at MOT time. Whats the mileage on your car?
If your mpg is low might be worth checking the spark plugs and giving it an oil service so you know whats in it to start with. A common problem on all Z's are air leaks in the intake rubbers and vaccum pipes/hoses across the engine. Air leaks will make the engine think its running lean and make it add more fuel at the injectors to richen it up. Its unmetered air that is being seen by the exhaust sensors that dosn't match what is reported as having passed through the Maf sensor. In diagnostics looking at live fuel trim data will indicate if they are high and suggest that it has air leak(s). Usual suspect is the intake rubber bellows after the Maf having a split in it, easy to replace if it is split. As to diagnostics there are threads on here with reccomendations, personally I use a Laptop with BMW INPA and BMW Scanner 1.4 and Gendan Engine Check Pro. I find BMW Scanner 1.4 the easiest to use but like Genden Engine Check Pro for live data viewing. BMW INPA is ok but clunky and can be a pain to install on a laptop without a lot of faffing around. Check out previous threads on the handheld scanner options others use.