No, this will not damage or cause wear on the struts in any way.
A Geo Metro is a front wheel drive vehicle. When a squealing noise occurs when the wheel is turning, it can be an indication of damage to the CV joints.
Your rear wheel may be squeaking when turning due to worn out wheel bearings or lack of lubrication. It is important to have it checked by a mechanic to prevent further damage.
could be struts and or strut brg plate that mounts the strut at the top
Does this squek vary with speed? When stopped and turning right does it squeak? More info is needed
NO That depends on how the struts attach to the knuckle or control arm. On some front wheel drives an alignment is required.
There are four suspension struts, one for each wheel, and two rear window hatch support struts.
Worn struts/shocks, tire out of balance, or bent wheel.
I have had the same problem in the distant past and could never work it out either, so I just started turning in any direction until it either became obvious that I was going in the wrong direction or the wheel stopped turning. Hen the wheel stopped turning I wound back a little and viola the brake was adjusted. Or just take the drum of and have a look.
Your ignition switch crapped on you
The Turning Wheel was created in 1954.
Static imbalance or an out-of-round tire or wheel. Can also be caused by serverly worn shocks/struts. Have the tires balanced and the wheels checked. Inspect the shocks/struts.
If only one wheel is not turning, this would indicate a serious problem with that wheel. Depending on if it was a driven wheel or not, it could be a problem with the brake, the bearing, the differential or driveshaft. Continuing to drive will likely cause damage to tyre, wheel, suspension or drive. It is also likely to have severe effects on the vehicles handling.