I'm one who strongly disagrees. If you grout that joint, it'll crack out. There's not enough moisture that the caulking can hold back that it would cause a problem before it has time to evaporate. This, as far as I'm concerned, is a no brainer that I've gone round and round with John (Bridge) on, as have many others in the industry.

What I see there now is fine. You CAN, if you wish, push in some fg insulation once the tub is in to keep the water warm as long as possible, but it's not necessary, nor is a vapor barrier or waterproofing on the tubdeck, although waterproofing wouldn't hurt.

First, the tuck tape. Look for "sheathing tape". It's usually sold in the box stores, sometimes it's red colored. You could use Tyvek tape as well. The vapor barrier is a bit tougher to diagnose. Your exterior foam, "expanded polystyrene" is usually quite leaky with regards to moisture transmission and is not a strong vapor retarder. "Extruded polystyrene" is a much tighter product, and it could indeed be a vapor barrier, probably a Class II barrier. If the exterior foam is indeed continuous on the walls and well detailed, then it might be best to omit the interior poly and just use the Roxul. Your walls may take in some vapor over time, but the vapor should also transmiss back into the bathroom during drying cycles. The biggest problems occur when you have two barriers and one or both are poorly detailed. Over time moisture gets in but has difficulty getting out. Thus the "sandwich" that you referenced. The "imperfect" in your system is the exterior foam. I'm a proponent of foam, but only if it is the right type and the proper thickness. With your exterior foam probably being a Class II on the exterior side of your wall, your best bet is probably to omit the interior poly and simply use other methods on the interior walls. You can use something like Hydroban in your shower (if the shower is on an exterior wall), it's a waterproof barrier but does allow vapor to transmiss through it. For the remainder of your walls, simply use two coats of latex paint over your interior drywall. Latex paint is classified as a Class III vapor retarder. As such, it'll slow moisture vapor transmission that wants to get into your wall, but if any does, it'll allow your wall cavities to dry out during a drying cycle. It's an imperfect solution for an imperfect situation. I'd be completely confident in my reply were your exterior foam thicker than it is and if I knew it was well-detailed. My concern is the interior side of the foam reaching dew point temperatures in winter and any moisture vapor within the framing cavity condensing on the interior surface of the foam, between the foam and the sheathing. That may not be a problem. But it is a consideration, especially since I tend to go towards the conservative side with an "over the internet diagnosis" such as this one. I'd certainly do more research if you can, you might get better information than what I'm offering. You are addressing moisture generation within the bathroom. That's good. Other stuff: 1) I do sometimes insulate interior walls, Roxul is good for that. 2) A simple yet effective sound deadener behind your washer and dryer is nothing more than a second layer of drywall over the first. 5/8" is better than 1/2" due to the added mass. Beyond that you can go fancier: 2a) sandwich a 1/2" sheet of homasote between the two layers of drywall. 2b) Use RC clips and metal channel between the studs and the drywall. 2c) Use green glue between the two layers of drywall. 2d) If you do research you'll probably see references to mass loaded vinyl, but I usually use that only when doing fully integrated sound deadening room "systems". I think you'd do better (and save money) with just using drywall.

You can keep the paper-faced insulation for your vapor barrier/retarder and for your tub surround waterproofing you can use a topical membrane like Hydroban (or an equivalent product) over the cement board, then tile on the Hydroban. Hydroban provides waterproofing, but it's not a vapor barrier.