Dandiya sticks are used in the Garba dance during Navratri, and a pair a child has wrapped and decorated themselves gets carried into the actual dance, not left on a shelf.
Plain wooden dowels, wrapped in ribbon, paint or paper and decorated however the child likes, become the pair of sticks used in the real Garba/dandiya dance during Navratri — a family or community dance, not a display craft.
Sticks a child wrapped themselves will not be neat, and that is not a problem — they will be recognisably theirs on the dance floor, which is the entire point.
Some families make a fresh pair each night of Navratri; others make one durable pair that lasts the whole festival. Either is fine — there is no rule here beyond what your own family wants to do.
Wrapping ribbon works from about four with help; younger children can still hold and dance with a finished pair.
A comfortable hand-length for the child works better than matching an adult pair — scale it to the dancer.
No — practices and length of observance vary by region and family. Ask your own community how Navratri is marked where you are.
Part of our guide to World calendars & interfaith families.