Steering wheel pulls when turning on a curve and my tires are wearing down because of this

Please check for a dragging LF caliper. Then be sure the front tires are at the same PSI. Then be sure the problem is not caused by the tires.*
Miss matched BRANDS,sizes or unusual wear patterns on one or both tires will cause a pull.
Tires look good? Rotate them,one side at a time until pull goes away.
Also, to see if it IS a tire problem,swap left to right and see if it pulls to the right.Easier to do that,first.

One more test: With you hands off of the steering wheel,start the car. If the steering wheel jerks to one side,you may have a bad /plugged spool valve inside the rack and pinion.

* I have seen that happen with NEW tires.

sounds like you have a bad wheel bearing, does sound change going around curves ?

Then your rack n pinion has a torque steer, before we go there is the tire pressure and wear proper, A low tire pressure will make the vehicle turn the direction that is low, also wear is it wearing on the outside or inside thos have to be look at.

get under the vehicle (use ramps) and check all linkages for movement pull push on the anti roll bar links, pull push on steering rack and pinion and linkages, any excessive movement, jack each wheel at a time, using a bar check the lower wishbone joints for movement, get the bar in the gap between the wishbone and lower part of the shock. and pull down, if any movement in ball joint up and down replace. while wheel on vehicle check for movement in bearing you will feel a tiny amount not much but pull and push on wheel with opposite hands on 12 o'clock and 6 o'clock and do the same at 9 and 3. now with both wheels off the ground but with the tyres still on, have some one holed one wheel and push pull on wheels each side there should be even movement between both wheels, if everything is fine with the the steering linkages and this dose not feel or sound right then this could be the problem also to add if the inside and out side of the tyres are wearing then the tyre pressure is wrong and needs adjusting to the right tyre pressure .

Camber and caster settings are off. Have 4 wheel alignment done by a good shop and save your nice tires. Out of alignment will make steering feel heavy and wear tires fast!

If you make a hard right or left hand turn (with steering wheel turned until it stops) you'll hear and feel a pop sensation.When you drive over potholes you'll feel a slight pull to one side.If it is one of the upper balljoints,you can grab the tire with both hands near the top(11 and 1 o'clock) and pull the wheel back and forth.You will feel looseness if the upper balljoint is bad.

If professional alignment does not straighten out alignment & tire wear, you can "tinker" with the settings to straighten it out. Caster is pre-set & non adjustable. You did not mention toe-in.(which more often causes wear. If the steering wheel is not horizontal it shows a possible toe-in problem, as can wandering. What condition are the tie rod ends and ball joints? Be sure everything is tight before doing anything else. If you make any changes, make small ones, write everything down and use good reference marks that will not wear off. Once a small change is made, drive for a while & check tire wear often.
You are correct in persuing this matter, but If you did not buy the car new, even a minor previous accident could throw the body out of whack enough to give problems like you are having.

I'm going to bet that you didn't do anything about checking the following:

1. Tie Rods and ball joints.
2. Shocks/struts...front and rear
3. Wheel balance
4. Condition of the tires.

If you don't know how to check the first two, do the following: jack front wheel up and insert a stand. Then take the bottom of the tire and pull up quickly and hard...does it 'click'? Now, do the same from front to back. Up and down wear is ball joints...side to side is tie rods. Get a mechanic to help you. Many chains will inspect for a modest fee.

If a tire is worn because of worn front end parts...the wheel can't hold a proper position in relation to the steering wheel...it wears the tires. They go out of balance and will shake at 25 mph. Check for rounded sidewalls and uneven wear. Replace the tires after getting new front end parts installed and aligned. Check your shocks/struts for excess wear or leaking. They contribute poor ride, to wear and sloppy handling