creating a half wall from full wall
 

I have a stairway to the basement which has 3 full walls dividing the living/dining/kitchen area (they make a surround the size of the stairwell). I would like to cut these 3 walls down to half walls 3' high but I am concerned that they may "wobble" since they only connect to each other forming a rectangular shape with one end open where the door is currently. Can this be done safely?

Are any of these walls "load bearing"?

Load bearing
 

No these walls are NOT loadbearing in any way...
If I may add, the main concern I have is whether the walls are solid enough that they don't "give" from side to side as some stair railings do when not constructed properly...

These wall are most of time bearing walls so what is holding up the floor upstairs?

There is no upstairs...single story house..these stairs go to the basement....looked in upper "attic" crawl space and wall does NOT continue above ceiling line.....

How about if you plywood the walls. Then, were they are free standing run threaded rod from the top of the knee wall through to the underside of the floor.

Have got trusses or hand framed rafters? Cut a hole at the end of the wall to run a 2x4 down between floor joists and block it solidly to hold your wall stiff.
I am still concerned about your roof, Evan if you have trusses you want to have a close look at those, because with newer houses, roofs change directions and some trusses are tri bearing. When or if you have something like this you will find 2 or 3 studs nailed together on the main floor and in the basement. Just make sure before you cut.