Will it help my case if wife let bf move in before we are legally divorced?

It certainly won't hurt it but most states are no fault.

In no fault divorce it does not matter. It's irrelevant.

If it's for child custody and he's a child molesting felon... YES!

Most divorce's today are what are called "no fault," because the other kind take up too much of the court's time. Check with your attorney, but in most states, it does not really matter, unless you are suing for divorce with cause.

If infidelity is the basis for divorce, it should. If infidelity is irrelevant and you are in a no-fault divorce jurisdiction, then it won't matter either way.

No

No

Ask your lawyer.