This engine is the same as the Carina/Avensis of the same period and all the parts are the same. Haynes covers both the cars. By the way, your car is AT200. The AT202 is the 2.0l engine.
You have got the part numbers correct. Have a look at the following link:- http://www.japan-parts.eu/toyota/eu/1998/celica/at200r-blmskw/3_252570_002_/tool-engine-fuel/1605_v-belt
Here are the links to the part number from Conti and Gates:- http://www.gatesautocat.com/drive/TOYOTA/Celica/AT200/7AFE/11-93_11-99/102839
Drive belts, ALT 5PK970, power steering 3PK628, AC 4PK860
http://aam-europe.contitech.de/pages/web-katalog/web-katalog_en.cshtml
Drive belts, ALT 5PK975, power steering 3PK630, AC 4PK860 - I fitted these actual belts to my old car.
The Gates cambelt kit which was fitted to my old Avensis is part number K015386XS, and includes the tensioner.
The discrepancies between the belt sizes are small, and the adjustments should take up the slack. Be careful when removing the crank pulley because it is has a rubber layer between the in and outer metal parts. Never use a puller on the out ring. Use the threaded holes. The pulley can cost between £40 to £300 to replace! Mine failed destroying the alternator and air-con belts. Lucky this happened as I left my house.
The coolant pump being driven by the drive belts and 'NOT' the cambelt, can be changed independent of the cambelt. I can be changed without touching the cambelt. This is covered in the Avensis Haynes manual. If it has been already changed and not leaking, then leave. You can decide.
The one good thing about the 7A-FE engine is that the engine is a non-interference engine. That means if anything happened, the engine should be safe. Some members have had broken belts and just replaced, like old Vauxhall and Maestro/Montego engines.