Hi--welcome to both BW and the forums!
To share my experience with my son: we started BW with him at 7 weeks. He responded really well to shh/pat. The patting was rhythmic, always the same; but he was flexible enough that the shushing could pretty much be at any rhythm. For example, I could do a shh-shh-shhhh or a shhhhhhhh or a SHH-shh-shh (sounds like a waltz beat ONE-two-three). The length of his winddown routine has changed a lot over these past 2.5 years. When he was really young, it was about 10-15-20 minutes. We'd sit and rock him for a little bit, swaddle, say goodnight to certain things (light, etc.), turn on the white noise, and shh/pat away on our shoulder and transfer into the crib. As he got older (as in 4-5 months), we'd read books beforehand, do everything else and he'd only need maybe a couple of minutes max of shh/pat. He'd go to sleep the rest of the way on his own. At 6 months, we'd pretty much stopped needing to use shh/pat at all and we'd weaned the swaddle. It was at this point that he was 100% fully an independent sleeper!
Hope that helps a bit...there's a process with lots of steps to get an independent sleeper, and it really depends on how old he LO is. If you're looking for more detail about a specific age, let us know and we can get more precise
Re: PU/PD and mantra crying, I don't believe there's anything on this site. But it does take practice to learn to distinguish between a mantra cry and other cries. Fortunately with PU/PD, you're right there with LO so there's no CIO. I could always tell my son's mantra because he would do a very rhythmic cry, pause for a little bit, then pick it up again. It was different from his upset cry--which I learned from doing PU/PD when weaning the swaddle.
Now, all of this re: my daughter...well, we're still trying to figure her out, but she's not a fan of shh/pat (!)