I am going to give it my best shot to answer all these questions, the pitching positions rule is one of the hardest to understand but this is what I have learned over the years.
1.1: I believe the second step you are referencing is as a result of MLB pitcher Carter Capps years ago where he would take a “jump step” in order to gain ground towards home plate on his pitch. Notice the jump that he does and that is now illegal under this rule. That is the easiest way to understand the rule. In words, the pitcher may not take another step towards home plate after lifting his foot to deliver the pitch.
1.2: Once again, Carter Capps would jump off his back foot resetting the pivot foot many feet closer to home plate which is no longer allowed.
Video: https://youtu.be/LycHv4CRHWY?si=BociY85PB1rQYVnI
1.3: The first step backward is referring to the common backward step that many pitcher do in order to get themselves in a position to throw the pitch. From the windup many pitchers take a step backward to put themselves in a position to throw a pitch.
Video of Yamamoto doing this backwards step: https://youtu.be/lQMyQ3PewOQ?si=-CnyobFWen4T568Q
1.4: The above comment and rule 5.07(1) are referring to different things. Rule 5.07(1) is saying that pitchers may take one step backward and one step forward (the one step forward is the pitcher lifting his leg to deliver the pitch). While the comment in Rule 5.07(a) is saying that the pitcher may not take 2 steps forward like Carter Capps.
1.5: No, in rule 5.07(1), it says you may take only one step backward, which would be your definition of a “rocker step” however, that term is not used in the rule book.
1.6: Under OBR the rule clearly says that the step must be backward, however, if you watch any big league pitcher many of them take steps to the side or even forward but that’s a conversation for another time. NCAA says that the step must not gain ground towards home plate. NFHS says the step may be forwards, sideways, or backwards.
1.7: When the rule says that “he shall not raise either foot” that is referring to before the delivery is started. When the pitcher takes a step backwards that is the start of his “actual delivery to the batter” which is why the rule continues to say that and why the step backwards is allowed. This rule does not apply for a pickoff.
2: Hopefully someone else can chime in because I am unsure about this rule as well.
3: Umpirebible is a great tool however it is very possible that it is either not updated, or that you may be looking at a different ruleset. I would stick with what the actual rule says which is “In the Windup Position, a pitcher is permitted to have his "free" foot on the rubber, in front of the rubber, behind the rubber or off the side of the rubber.”
Hope this helps.