Im trying to replace the alternator on a 1999 Mazda 626

When you say everything goes dead are we talking all lights, radio, wipers? If so, main power or ground cables bad or fusible link. If just engine, check coil, ignition module, crank/cam position sensor.

okay, good testing, your next step is to check for spark, remove a sparkplug wire and insert a screwdriver into the boot and place near a metal object like the engine and see if it sparks. let me know if you are getting spark and we will go from there. good day.

Probably low fluid, check for leaks and fluid level.

No. If your starter is whirring but not turning the engine, you're going to need a starter. The belt is irrelevant.

Sounds like a possible starter problem if the starter will not turnover the car's engine when hot. Change the starter.

have you replace the timing belt ?
have a mechanic check for worn bearings

You may have to dig deeper for a vacuum leak. It's possibly the intake manifold gasket. Try spraying some starting fluid around the intake manifold. Also try disconnecting the brake booster and plugging that hose, the diaphram in the booster could be ruptured, causing a vacuum leak. Check the PCV valve and hose too.

on this websites you find fuse box diagram and description for Mazda 626 (1999)
https://www.carknowledge.info/mazda-626-1997-2002-fuse-box-diagram/

https://www.autogenius.info/mazda-626-1997-2002-fuse-box-diagram/

Remove cables from alternator. Loosen tensioner bolt. Remove belt. Replace alternator. Replace belt. Tighten tensioner bolt. Replace cables and done. Mike. Rate 100% please.