1 - I replaced the 6 pins holding the three flat rails; the seventh is a large, loose fitting pin at the base of the curved tensioner rail and is easily removed once the cover bolts is removed. As mine was not corroded, I did not replace it.
2 - The pin puller works because you are screwing a bolt into the rail against a fixed collar (I used a socket). As the bolt enters the pin (which has a female thread) it eventually abuts the collar and wants to cease going in any further. You keep turning it (some force required) and as the bolt cannot compress the massive socket, the pivot pin is subjected to a pulling force to which it yields by exiting the engine cover, entering the socket (make sure the socket orifice is large enough to accept the pin). The key is that the bolt head must contact the base of the socket before it reaches the base of the pivot pin thread, or you will just be forcing it into the pivot pin without generating any pulling force. You can only generate pulling force on the pin when the bolt head contacts the socket base before bottoming in the pin.
A related problem is that some of the pins are very close to webbing on the engine cover, preventing your socket from mating at right angles with the engine cover. I used (but did not illustrate) washers to pack that side of the socket not in contact with the engine cover. A better approach is to grind off part of your socket head to a depth of 4mm or so, to permit a flush fit.
3 - If you are also replacing the tensioner because the old one is weak, it may be a little easier to replace the rails with the old tensioner in place. As regards the chain/rails order, I can't think it makes any difference. Note that I changed the rails and tensioner first, thus allowing me to determine whether the chain needed to be changed. Once the new rails and tensioner are in, the major sources of out-of-time should be wear in the chain ('stretch') and the toothed gear wheels on which it runs.
I ended up replacing the chain on the 380, but not on the 560. If it ain't broke, dont fix it....