From the same law (p. 1):
(bolding mine)
So, apparently nowadays “even with the ball” is OK.
The laws of the game will always prove to unable to keep up with the dumb ideas of some referees. ( *I can say that cause I used to could spell referee and I were one and I stayed at Holiday Inn Express last night * )
Watching a under 16 boys tournament, a young man took off dribbling the ball from his own half of the field. There was only one defender near and her out ran the dribbler and got ahead of him. All the other players were still getting back from the set piece that allowed his team mate to pass him the ball near the half line.
Anywho, they did a bit of did a quick ‘doesy doe’ and the man with the ball was goal side of the defender facing him. He flicked the ball toward the goal and then spun and got to the ball before the opponent. The referee blew the whistle and called him offside because there was only the goalie between him and the goal line.
We all howled in protest. He said that the player had received the pass while in an offside position so… He said the player passed the ball, not just played the ball. He passed himself the ball and so the offside rule applied. That team still won but if they had not, the referee would not have survived I think.
:: Remember, the other players were still not near and no one else was even near or trying to go for the ball. ::: Sometimes I hated doing assessments for upgrading referees. ::
Um, what part of the word “originally” did you fail to comprehend? 
The history of the laws of the game given by FIFA does not mention that the ball had to be closer ever. The other sites I have looked at agree that to be offside, the player had to be closer to the goal line than the ball.
Regardless what you think you recollect, all goal kicks prior to the 1997 rule change were “indirect,” that is, you could not score directly from them. I have numerous copies of the Laws for the period 1986 to 1996, all of which make this clear with the statement, “A goal may not be scored directly from such a kick.”
Either they were not goal kicks, or someone else touched the ball before they arrived in the opponent’s net.
No sure, but I think it’s the same as the part of “nowadays” that you missed… 
In the Spanish and Portuguese soccer speaking world it is referred to as a gol olímpico, or olympic goal. This came about because the first widely recorded goal happened in a 1924 game between Uruguay (who had just won olympic gold) and Argentina. Ironically the goal was scored by an Argentine Cesáreo Onzari. The Argentine press dubbed the goal an Olympic goal to poke fun at their cross Rio de la Plata Rivals.
As to the corner kick off-side exclusion, it did come from the old off-side rule that stated that a player in line with the last defender was offside.The key words were that two opponents had to be nearer their goalline than the receiving player (equal is not nearer). THis rule was chaged in 1990 by adding a caveat:
- A player who is level with the second last opponent or with the last two opponents is not in an off-side position