That's a lot of new information I didn't know, I am glad for the sharing.
I was streaming a 'research' run few days ago, and you can watch the video now. I tried to list all the rank decreases, boss par time, boss destruction bonus, and few moments that clarify it's only Front Flame that gives a score for dealing a damage.
There are obvious wrong sentences in my guide now with all the new info, so I need to modify them!

Including losing a heart not causing score loss - I think I was not aware of the penalty at the moment I saw the score decreasing. It's probably that the penalty just got into action right before I died that made me think that way.
Boss Time Penalty (I was keep calling this 'Par Time', after seeing one 'concept' entry in Giant Bomb with the same name - I think I am gonna keep saying it that way just because it's a familiar term to me now) is -1 score/frame. When you make the game go crazy enough, it ends up only giving -20 score/sec(?). So I think it's depending on whatever smallest time the game can run on, instead of frames. There are few moments where the game doesn't constantly give defined score penalty, and trying to do double on the next frame. Like, the first-digit should go 0-7-4-1-8-5-2-9-6-3-... but instead it sometimes go like 0-7-4-4-8-5-3-2-6-...
Tower B (Stage 11) first boss's first phase, two orbs, are separately counted toward Par Time. So when you exceed a Par Time in this phase, you always exceed two at a time, as long as both orbs are alive.
I am happy to know that you are telling about the bomb not instantly go off the HUD. I thought I am keep getting score too low, and there were moments I use a bomb to buy a new bomb instantly after, while I am having a full stack.
Money
I doubt testing the crystal rank impact would be easy - crystals not retrieved are shown in just few pixels, and then - if my guess is right, that they stay visible 'then' invisible - become invisible for a brief time until they're truly gone. So I don't think you can see a crystal actually disappearing... I hope my run video would help seeing if this is really the factor to the rank.

Crystals will likely become invisible faster if you deploy more than 3 weapons, just like how treasures not retrieved disappear for the same reason. But like the treasures, crystals disappeared this way will return back to the visible state but they will eventually become invisible - again if my guess on 'first stay pixels then become invisible' is right.
I started to think that the graphic shown at the moment you buy is the upgrade you get. And each weapon upgrade has 5 graphics cycling, so total of upgrade for each weapon could be 5. I think I saw Down Sprinkle upgrade only showing Twin Laser graphic in later game, but I need to confirm after watching more videos.
I have yet no idea about what Bomb Level upgrade would actually affect. My guess is it increases the lasting time. I need to watch more videos for this one too.
Animal
I was thinking that one full plant fills up a fifth of the animal soul gauge, so I think you're right on the exact number.
I was happy to find that some stages with abnormal scroll direction is not just the graphic! The same way you described, the scroll affects the trace of animal on City B too! When the scroll briefly stops, the animals will also not scroll away! In Stage 11 I tried to kill popcorn enemies and La.Gorilla (the big ones with two arms) behind them so I get most of the animals. It is certainly dangerous to do.
Time
This is the reason why I want to call my guide just covering the basics. Such insight is something I can't provide by my own!

I have no clear observation on the scroll speed at the moment...
Other things
Shopping
I am pretty sure I tend to buy life at full stock in my earlier runs. I need to watch my early runs again to see what changes.
Stage 11
First time I thought the bosses are tied to each route, then I saw Kachirou getting Acidic Princess in Route U, where I always get Paladin Kilauea. It could be related to rank or something else... Butler and the Princess were the rarest one I could see in my runs.
Routing
One of my runs ended with the Double KO Momoko. I got the boss destruction points, but the game ended after.
Real Talk
At least I am really happy for having Route U, I didn't know it's a randomized route. It's sad to not have all stage routes though, and that even in 'two full area' routes you have to listen to the same music 2~3 times because all stages in an area mostly have the same stage music. I really hope Shohei could make stage music for all stages and that is included in the game in similar to how M2 includes various soundtrack to each game. All we get is just suspiciously named 'Rejection' tracks.

Momoko's few patterns really killing me, they're single-handedly killing all my clear attempts recently, do you know how to properly handle them?

Also I want to post my guide on this forum, but I have no idea how to properly post it there: I tried to find the meaning of those acronyms for an hour and then gave up.
