Do I have to remove the center nut to replace broken lug studs

jack up vehicle, remove tire. knock out old stud with a hammer and punch. put new stud in from back if need be. to draw it up tight.use a lug nut with something under it so when you tighten the nut it brings the stud into position. remove the nut you put on. and replace the tire. good-day! if the brakes and rotor are in the way. you will have to remove them to replace the wheel stud.

THE INNER STUDS FOR THE INNER WHEELS ARE NUTS AS WELL AND SECURE THE INNER WHEEL. USE A SQUARE DRIVE TO REMOVE THESE STUD/NUTS. DRIVER SIDE NUTS/STUD ARE LEFT HANDED(STAMPED WITH A BIG (L)). AND PASS SIDE RIGHT HANDED. THESE TORQUE SPEC OUT @ 400-450 LB FT. OF TORQUE, YOU WILL HAVE TO USE A CHEATER BAR OR HEAVY DUTY INPACT!

Lugs?. I guess are the wheel studs(Im in australia)
First see if toyota sells the lugs separately, if yes you can use a punch to remove the last broken bit, the new ones are installed by packing with washers and using the wheel nut to pull them back into place.
If you cant buy lugs separately, you will need a new hub from the dismantlers

remove the control arm and the upper ball joint, possibly the tie rod too. your gonna need a air chisel more than likely.

There are 4 bolts holding the wheel bearing/ABS sensor Assembly to the axle housing. Remove them and remove the wheel bearing from the car. You will be able to rotate the spindle and remove the lug studs. To replace them put it in the hole and tighten a lug nut to pull it into place(an impact wrench will be quite helpful). No Hammering it in, as it may dammage the sensor or bearing.

They are replaceable.
You can knock the broken studs out with a point chisel (wear safety glasses). Take the pieces and nut to an auto parts store in order to get the same nut size (don't want to use two tire tools/wrenches).

Half right...pound out, use a stack of washers and put nut on backwards and draw stud in. Oil on washers and stud threads helps.

I might try a different shop. I have never heard of a broken Stud nut making any noise I hope they diagnosed a problem with the noise. Also in-experinced tire tech's over tighten lugs with their impact wrench and snap broken studs

You can remove old lug by driving it out with a decent sized hammer. To re-install, push new one into flange from backside and stack washers on wheel side, leaving enough room for the lug nut to go on. (backwards...flat side in) Tighten the nut, pulling the lug into the flange, till it is flush (like the unbroken ones) I suggest that you put some lube on lug threads to prevent binding while doing this.

pick up new wheel studs. using a punch hammer out the old broken off studs. push in the new studs from the back side grease the threads put your lug nut on backwards and tighten up this will pull the stud into place. as long as your wheel isnt damaged or new wheel . use a torque wrench and torque the lug nuts drive a mile or so and torque again and then after 50 miles.