not one to backup my information on hearsay:

everything below is tested in battle:

question 1:  when is the item spin code started?
answer 1:as soon as the game is loaded
proof:  i couldn't replicate the results at any time in between the nintendo screen and the is this ok? screen.  this was after about an hour and a half of trying.

answer 2:  exactly as the lakitu traffic light screen is loaded (the physical appearance of the item spin box starts at this time, but the actual code may or may not start before the screen is loaded.
proof:  before, i believed it was either when the screen was loaded, the light turned green, or before i ran over the first item.  when i saved at the character select screen and used the boost start to grab the item straight ahead on course 1 and course 2, i was able to replicate (10 times same item) the results without conflict.  i just used the track designer and was able to edit battle course 2 making two extra question marks (one below player 1's starting position and one two pixels ahead).

question 2:  when is the item variable assigned a random value from the spin code/spin code is temporarily ended?
answer 1:  as soon as you select "(yes)" in the "is this ok?" game mode screen.
proof:  i saved state each time i was able to push b (loading up the 1/2 player option, game mode option, confirmation, character select screen, character select confirmation, course select/confirmation)  i started from the course select confirmation and worked backwards.  this took the majority of the time.

answer 2:  as soon as you select change course, retry, or change driver in the loss screen.
proof:  i saved state at the loss screen.  i was only able to replicate the results (the first item i chose from the same question mark (straight ahead on course 1 and straight ahead on course 2 for player 1) was always the same) while saving state as i selected an option from the loss screen.

question 3 (battle tested only):  are player 1 and player 2's spins controlled by the same line in the code?
answer:  no, there is a delay for player 1
proof:  player 1 and player 2 yield different items >90% of the time when both players start on a question mark.  if the item box is significant to the real code, player 1's item spin starts a frame later.  this can explain why both players will have the same item less than 10% of the time (assuming both players hit their first question marks at the exact same time).

question 4:  can you stop/time which item you get by pushing A when you run over a question mark?
answer:  no (battle and race), the items have been preset at the beginning of the race (battle only).
proof:  i saved state right as i ran over an item.  i let the item box stop by itself, pushed A immediately, and waited 2 seconds before pushing A.  all return the same item.  
i saved state a few pixels before i ran over an item.  if i changed my velocity, i got a different item (sometimes, the red and green will not change, but this is due to the fact that red and greens are more frequent than other items in battle).
for relatively every frame, the item box displays a new item always cycled in the order feather, star, banana peel, green shell, red shell, ghost and mushroom.  however, green shells~33% and red shells~33% are the most frequent, followed by banana peels~13%, and the numbers for the rest are similar 5-10% each (i have the exact stats from 80 games on another computer).  

question 5:  how does the item/spin code work?
answer:  i'm not sure.  what i do know is the item box order is probably not how the code is randomized because i can't predict what item will be randomly assigned at the selection screens before each game.  i might be able to test this in game if i had the time(Ha!)  from the statistics of item frequency, we can probably figure it out.

this isn't the last word on this subject.  there are many other tests to do, especially in match race (because match race is place and maybe course and lap dependent, it will be quite complicated).  grand prix will also be exciting considering 8 different places if anyone wants to find all item chances for all 8 places.  my work probably has errors or needs to be clarified (though i did not create ad-hoc explanations or use circular reasoning no matter how tired i got).

thanks.

p.s.  i found a new move for anyone who enjoys battle mode.  i'll post a video later.

1:10 AM : begin test
9:13 AM : finish tests and post
9:14 AM :  thankful i copied my post before clicking post (message too long)