@George P. Take a look at the varying opinions/approaches you have received here...this is exactly why it behooves you to bring in one or more qualified professionals, licensed, bonded and insured, who will pull a permit and go on record as having done the proper work and stand by it with his/her money.
Just because the wood is rotten and not supporting anything does NOT make it safe and negligible. In fact, on an outer wall, which is carrying quite a bit of load, it may be beguilingly accessible. Also, keep in mind, you are placing quite a bit of trust in the builder(s) who have preceded you. There is no guarantee everything is built to handle what you are expecting it to. Finding out with a live body and money can be regrettable.
As far as sistering the studs, what is the incremental cost for using a properly sized stud in dollars and time? Are you really saving that much and is it worth the risks? Not for me. I can see leaving as much of the old stud as possible because the facade is attached to it (and it provides more surface area for interior wall hangings), but I prefer a continuous stud from the top plate to the bottom plate. Be certain to use a moisture barrier between the bottom plate and concrete, and even consider a pressure-treated bottom plate.
As far as messing around with the facade, I have not yet worked with one personally, so I would work with a pro first to learn more before I begin tackling it solo. That's one of those things that when it goes wrong, it probably goes big.
Our philosophy is that there is the right way(s) to do something, and varying degrees of the wrong way. Ultimately, everything comes down to someone must pay now or pay later. Many real estate investors I've met are so married to their numbers that in spite of loads of great advice, they are still going to do what they wanted to do. That said, I wish you and all subsequent users of that property the best.