The speedometer is broken where can I buy the part

If just the inner part is broken, remove both ends of cable, pull out broken parts. Buy a universal repair kit at parts store and follow instructions that come with.

Sounds like a fuse to me it's very rare for several components to fail at the same time however one fuse can run several areas of a vehicle.
The fuses and their locations also a list of what they cover should be at the back of your owners manual if not you could do a search online under fuse locations for your model.

Change the speed sensor if you have the electronic speedometer. If you have a cable driven speedometer, buy a new cable, and replace the old cable if it has been broken.

The speedometer or the speed sensor are broken. Buy new parts here:
Speedometer:
http://www.woodfins.com/Parts/2008-TOYOTA-YARIS-83-R119-273-Speedometer_Instrument_Cluster.html

see if it is attached at the transmission or if it has come off on the back side of the speedometer if end of cable is broken then you need to buy a new on at the auto parts store.

if the speedometer is working but the counter is not - then the counter gear is broken.
it is not worth trying to fix -- just buy a new gauge and install it.

c...

as far as the tabs you can buy a plastic glue at the auto parts , it is an epoxy two part that is in a dual shringe like applicator. Its really good.

THE SPEEDOMETER CABLE GOOD AND SPEEDOMETER NOT WORKING.2 POSSIBLE CAUSES WHILE ITS NOT WORKING SPEEDOMETER GAUGE BROKEN OR SPEEDOMETER DRIVE GEAR IN EXTENSION HOUSING BROKEN.

The most likely problem is the speedometer cable is broken, probably near the transmission. if it's the cable, probably under $10. Disconnect the housing at the transmission, and the cable is inside. Pull the cable out, it should be square at both ends. a broken cable is obvious. insert a good cable (with some appropriate cable lube) into the flexable cable housing, you might have to turn the cable a bit to get the end back in the speedometer. If it is broke , you will also have to disconnect the housing at the speedometer to get the other end out. You might be able to reach it from under the dash, but you might have to loosen the instrument cluster to reach it.

Buy new speedometer. Try some junk yard or toyota dealer . Should be an relatively easy swap