I would like my NEW contributions to go into a Roth 401k while keeping my previous contributions in the traditional. Can I do that?

It's likely you can but each plan administrator and plan has different rules.

If they say yes, then no taxes on the current balance today.

You might also be able to slowly bleed the traditional into the Roth. This way you can transfer in the account per year and slowly convert your tax consequence as need be, but this would be up to the plan administrator. This ability is less likely but it's worth asking.