I bought my first house in 1993 in San Leandro, CA. It's right next to Oakland, in the East Bay. The house already had 2 layers of shingles, but the home inspector said that the roof was bad. On the advice of my realtor, I had the buyer install a 3rd layer. In hindsight, I would never have done that, but I was young and still had a lot to learn about houses and real estate.
I sold the house in 2002 when the housing market was going crazy, and I was expecting to have to put a new roof on it, but my realtor said that they can ask, buy you don't have to if I didn't want to. They would either have to agree to buy the house as is, or walk away.
I've always felt kind of guilty selling that house with 3 layers on the roof. I should have insisted on a tear off when I bought the place. Since then, every house that I've bought, I've stripped the roof, fixed the decking, installed new flashing and 50 year shingles.
You do not need a layer of tar paper for the second layer of shingles. The biggest issue is in using nails long enough to fully penetrate the decking. The shaft of the nail is where the holding power is, so the point has to be fully exposed through the decking. The point has zero holding power.
Short nails are cheaper, and it's a common way for roofers to save a buck. Staples are cheaper, and if installed properly, will hold better, but they are IMPOSSIBLE to consistently install properly because the thickness of the shingles changes with each row, and if a staple cuts the shingle, it's WORTHLESS!!!!
If the decking is bad, the nails will not hold. Plywood is great when it's brand new, but once it's been nailed, the bottom layer has a tendency to blow out, which doesn't leave enough wood to hold a nail. A very detailed inspection of the underside of the decking needs to be done before you go forward with a second layer. OSB doesn't blow out like plywood does, but there is also a limit to how many times it can be nailed and still hold a nail. If it's older and solid wood was used, like 1x4's and 1x6 pine, there is always areas that have broken off and there isn't any decking there at all.
Brand new flashing is super important if you want your fascia to last. Rotten fascia and soffits always start from bad flashing. It is pretty much impossible to replace the flashing and leave the original roof on.
Whatever the rating is for the shingle, cut it in half for the second layer. Because it doesn't lay flat on the first layer, it ages a lot faster. 30 year shingles should last 15 years, but they will be pretty ugly by then.