The rules say that the timer starts when you touch the first squidbot. Does that mean that I can collect all the reels that aren't from squidbots first and then start the timer?

Of course not but I forgot that you can get some reels just by finding them. So, I modify the rule to:

"Timer starts either when you collect a reel normally (when "1" pops up) or when you touch the first squidbot and ends when you collect the last reel (when "105" pops up)"

I hope this rule is understandable. If not, let me know. Anyway, I let you choose which "kind" of reel to start with.

Still regarding the all reels%, can I finish the game without collecting any reels and use the same game file for the run?

Yes, please use a save file with all levels already unlocked/available. I updated the rules for this.