I don't think it would be improper at all to ask your coworker out.
Sometimes when a person has went through a tragic event in their life, it is best to be in the comfort of those who truly understand how you feel. As someone who knows exactly how you felt (and still feel), he may turn out to be a great friend, and who knows what more?
I am not saying you want a relationship with this new guy...but for the future....I am sure Justin would want you to be happy. If he loved you and wanted the best for you, he would want you to be strong and have a happy, fufilled life. Your heart may love again, but it can never forget.
Don't worry about what others say! There is no right or wrong amount of time to heal. As long as you are true to yourself, then that is all that matters.
As for the ring, I say keep it, cherish it, and remember that you were blessed with his love, and you still are.
You are such an incredibly strong person!
If you need anything, just PM me....
Ivory