the biggest advantage I see from a papal coronation is the ability to choose successors or was this law altered at any time after Charles V
maybe they didnt want the protestant princes to feel alienated ? shouldn't have been a problem after peace of Westphalia since Cuius regio, eius religio
easier to bribe/influence electors than pope ? they already had bohemian vote. it would be easier to get the three catholic bishoprics votes given that habsburgs were always mostly catholic. I dont know if any of the three bishoprics turned protestant afterwards
would it have been difficult to influence the Pope becuse of house medici(3 popes + papal bankers + two queen regents of france ) who were closer to france than austria
Popes influence decreased since the reformation and they didnt just care that much about the pope?
point out any mistakes i made in my assumptions
The cessation of the requirement for a Papal coronation to crown the (elected) King of the Romans as Holy Roman Emperor occurred in 1508 under Maximilian I. Quoting Norman Stephenson's "Paw Prints Along the Rhine":
The King [of the Romans, Maximilian I] then set out to Rome to secure his own coronation, but Venice refused to let him pass through her territories; and at Trant, on the fourth of February 1508, he assumed the title of Roman Emperor Elect, to which he received the assent of Pope Julius II.
In effect, Pope Julius II assented to a new title (Electus Romanorum Imperator) - Roman Emperor Elect - that conferred all of the (by now, largely prestigious) powers of the Emperor to the King of the Romans without the requirement for a Papal coronation. As you point out, only Charles V would go on to receive a Papal coronation and was therefore the last Holy Roman Emperor to be crowned without the technical qualification.
In response to your other questions, many of them are addressed in this recent thread around the election processes and powers of the Holy Roman Emperor: https://www.reddit.com/r/AskHistorians/comments/884iwg/why_were_austrian_habsburgs_nearly_always_elected/
If you're interested in this period, I suggest checking out "The Richest Man Who Ever Lived: The Life and Times of Jacob Fugger" by Steinmetz. Its a biographical account of Jacob Fugger, a wealthy financial trader, who played a key role in securing the elections of both Maximilian I and Charles V. He was basically an early Rothschild-like figure seemingly forgotten by history.