Hey Yeves!

Unfortunately there's not a lot of info other than these speedruns readily available out there. You've listed a lot of good ones, but I'll elaborate on those a bit.

LIVES: If you get 8 or more lives, the game will let the enemies out of the bubbles sooner and summon the white whale sooner. Hearts also count as lives. I recently ran a 27:16 run with like 17 lives at the end, so it's not to say you HAVE to die to keep the life count below 8...just that on some levels it might help you manage item drops or other enemies and keep the enemies in the bubbles longer.

STAR ROD: Probably the most important one for an Any% run. NOT collecting 7 crystals will (typically) summon the star rod on the next level after the 7th skipped crystal. I think there are two possible ways of where you ideally want to get the star rod...

 Level 41:  If you can get the 7th crystal to spawn on level 39, a star rod will appear on level 41.  This will let you skip levels 41-60, including the bird boss fight AND the basketball mini game.  It'll plop you right into Level 61.  The later levels are tough, but skipping the boss fight and minigame are huge saves.  I've done this method before I really knew what I was doing in the game, but have not gone back to try it out again. Your first 40 stages will need to go a bit slower to get that many crystals to show up.

 Level 61: By getting a 7th crystal on level 59, the star rod will appear on level 61 and skip you to level 79 (Super Drunk fight).  A crystal on 61 is not the worst either, which is what i got in my run.

 * Just an FYI, if you happen to get the 7th crystal on like, say, Stage 57...the star rod would show up in level 58, and only skip you to Level 61.  It just moves through the next boss fight and minigame (or to the final boss fight), depending on when you get it.

ITEM DROPS: Ok...some of this is pure guessing or conjecture. I also don't know which items trump other items. This is the biggest question mark in the game yet, but a bit has been figured out. I won't list all of the items here, just the ones that I typically see in a run. SHOES: Typically bouncing on bubbles 5-6 times will spawn a shoe. If an item has already spawned in a level, the shoe will typically appear on the next level, unless trumped by another item drop. HEART: This seems to be tied to the amount of food you pick up. Not 100% on the amount needed to spawn one. CANDY: Not sure on this one. Amount of bubbles blown/popped? Jumped on? CRYSTAL: Not totally sure here either, but it seems there's some element of time related to this one. Spending more time on a stage, or hitting a certain game time, sometimes causes a crystal to pop up. Sometimes some food needs to be collected before the crystal will come up. UMBRELLA: After collecting two shoes back to back, an umbrella typically appears in the next level. Sometimes this doesn't happen, but the game will delay the umbrella drop until other item drops have cleared out. It seems to be counterproductive to keep trying to get shoes if you get 2 back-to-back and the umbrella doesn't appear in the next stage...the umbrella just kinda comes up when the game's ready for it. Sometimes the game will give you the umbrella if you don't collect the shoes back to back, but I'm not sure how that exactly works either.

MISC: The only other thing I try to make sure to do when running is end the level as close to the lower left corner as possible. It speeds up the transition between stages. Not a huge deal, but it adds up over 40-50 levels.

Anyway, I think that's most of what I know right now. Maybe you already knew that stuff too, but at least it's here for anyone else to start with if they'd like to try the game. If anyone else knows other info about the drops or game, please feel free to chime in!