JKR has spoken to this issue on a number of occasions;
The most instructive quote is probably this one regarding wands and family allegiance:
Stephanie: If the wand chooses the wizard, then why do wands work when passed down from father to son eg neville had his fathers wand
J.K. Rowling: As established by Ollivander, a wizard can use almost any wand, it is simply that a wand that chooses him/her will
work best. Where there is a family connection, a wand will work a
little better than a wand chosen at random, I think.
It follows that not only would Ron be able to perform magic with any wand, but that Charlie's old wand would also probably be slightly more effective than another wand.
As to what happened to Charlie, the clear implication is that he has a new wand and that Ron, as the youngest wizard in the family now has to accepted his hand-me-down.
Ollivander repeatedly reminisces over people’s first wands, suggesting that replacing them (presumably when they wear out or become broken) is at least a semi-regular occurrence in the lifetime of a wizard.