Since most of the questions were answered already, I noticed that this isn't quite answered.
Another concern I have is how fees would work and when is the optimal time to withdraw to a private wallet.
You know for the fees could be dependent on how much you need the money. If it's right away or not. If you are not going to be using the funds immediately, then you could opt the lowest fee and that transaction can go on unconfirmed for a couple of days or weeks. If you need it right away then the highest fee would be the best.
Either way, there's nothing wrong to withdraw from your private wallet. It's better that way.