(1) The Tur rules like Rabbeinu Tam that if the liver was salted, it may be cooked even with other meat, however it is customary not to do so in the first instance, but post facto it is permitted. The Sharei Dura writes that even post facto it is forbidden, however if a Rav ruled like the Rabbeinu Tam we don’t contradict his ruling. It appears to me that even if it wasn’t cooked yet. the Rav may be relied upon. However if it was cooked with other meat, without having been salted, everything including the pot becomes forbidden unless there is sixty against the liver. The Tur writes that post facto, a liver that was cooked alone even without having been salted is permitted. Therefore, if a Rav ruled like the Tur we do not contradict his ruling.
(2) This is only according to those who rule that one need not cut open the liver if it is to be roasted. However according to those who require it even for roasting, merely piercing it is unacceptable. One should be stringent even with the liver of poultry to at least make holes in it. It is best however even regarding the liver of poultry to cut it along its length and width, it seems to me that for the liver of poultry, it suffices simply to remove its gall even if it is to be cooked after roasting. Regarding the liver of other animals however, it must be cut along it’s width and length if it is to be cooked after being roasted. If it is only to be roasted, piercing holes in it will suffice.
(3) However initially it is forbidden because there is a view in the Gemara that if the liver has been extensively cooked, it is forbidden. We are not experts who can determine what !s considered to be extensively cooked or not.
(4) This is the view of the Rambam who holds that even the liver absorbs. Most poskim however hold that it doesn't, and are simply acting stringently like the Rema. We should rule like the Rema and forbid it.