Another bird question. Can my budgies play with cotton balls if I string them on yarn or rope?

I don't think so.

I would see no issue with the cotton balls...people often put out cotton for birds as a nesting material. However, be careful with the yarn or rope...that could be an issue if it got tangled up in their feet...though that's unlikely.

life, common sense

with claw ? maybe ..

Yes they can. I give my birds cotton balls, socks, toilet paper tubes to play with.

http://zoocrewkids.blogspot.com/

No, it will give entangled legs, legs will be broken

Yarn or rope cannot be used in any lengths longer than one inch. Many a bird has hung itself getting caught up in rope, yarn, fringing or string. pets question and answers,www.5d2d.com
In regard to cotton balls, remember they are bleached, and also if the bird ingests any then they can get an impacted crop.
There are far better and safer toys for birds.