Even though I have made (three versions of) the rygar timeattack, I have to admit that I might not know 100% of the little details of the game and there perhaps may be some things I have missed. But about your suggestions:
1) Unlike in many other NES games in Rygar the items are not dropped by the monsters randomly. It seems that each 6th-10th (or something similar) monster drops an item and there doesn't seems to be any way of influencing this frequency. You can influence which item they drop (star or bottle) with a small probability, but that's it. In the timeattack I had to sometimes make rather long parts again because the monsters were dropping a bottle when I really needed a star. No simple variation in movement seemed to affect this, but when I played a longer part again, it changed to a star.
2) Honestly I don't know if the thumping sound is directly related to the monster getting damage. It probably is, but the first time I tried killing the forest boss I did it without autofire. The second time I did it with autofire, and it died almost twice faster. It may be that the second time the autofire helped make more hits in the same time (even when you can only make damage at certain intervals).
Anyways, it's very difficult to optimize those triple-fire-thingie-throwing monsters because you need to constantly predict when will the next one be shot to jump over it. If you jump too late, you get hit.
I'm not saying it's not possible to optimize those boss battes, I'm just saying that if it's possible it's not trivial...
3) If this was a smb-type timeattack where you are optimizing even single frames away (which IIRC are about 1/20 of a second in famtasia) that would certainly be true. However, since this is such a long game and the random nature of the game may cause several seconds slower or faster runs each time anyways, those fractions of seconds probably don't affect the overall time in any drastic way. It's certainly true that I might have saved fractions of seconds here and there, but they all probably sum up to a few seconds in total (which could then be lost with an unlucky random monster placement later or whatever). Rygar is quite a laborious game to make a timeattack for... :)
4) Rygar is too close to the wall at the start of the spider boss screen, so he must run some distance to the right for the ducking tactic to work. Also, you can't hit the spider right away, when it's coming towards you because it will change its direction and start going away from you, thus you have to wait for it to get to your left. I don't believe running a bit to the right, ducking and waiting for the spider to get to your left saves any time compared to the jumping (or if it saves, it's some fractions of seconds).
5) This might actually be true. I have never tried it. Could save a couple of seconds if it works.
6) The Dorago boss is difficult as hell. In the first timeattack I made it took me (IIRC) more than an hour to defeat it, and it resulted in a 3min 20secs battle. In the second timeattack I optimized the jumping better and was able to drop it to 1:40. In this third timeattack I was able to optimize it even further to 1:20 by not jumping so much to the other side. It may be possible to optimize it a bit more, perhaps even 5-10 seconds, but it's a very difficult one. Those projectiles make it quite difficult.
7) I thought it was impossible too, in my first two timeattacks. In this third one I tried it again, just in case, and to my big surprise I found a tiny spot there under the rope where you could jump from and it would reach the other side, which saves quite some seconds compared to having to go around the river. The second time I had to cross the same river in the same direction I just didn't find the spot even though I tried dozens and dozens of times, so I just gave up and used the rope instead. (Btw, if someone doesn't know, the rope can't be used until you get the hook from the end of the forest level.)
Everywhere else I have tried jumping over that kind of gap I have failed. If there are other places which such a peculiar feature, I was unable to find them. It might have something to do with the rope itself: Perhaps the game engine adds something there where you can stand on and which usually isn't there.
8) The snails shoot more often than the forest boss and they are even more difficult. It might be possible to optimize those too, but it's not trivial.
9) I never take damage on purpose. I always try to find a way to run without taking damage without slowing down more than perhaps a fraction of a second.
The 15:34 situation is much trickier than it may look from the video. The flying monster is too high to be hit while standing, so the only way of hitting it would be to jump. If you jump, however, you must just jump on place, without advancing (because else you just fall to the gap and die). It's not possible to jump the gap, you must use the rope. Also, the flying monster is too far away to be hit if you jump before the rope (and try to hit while falling back to the ground). I tried tons of things there, but couldn't find any way of solving it fast, so I decided to take the damage instead of spending more than a second jumping without advancing.
My principle has always been to avoid taking damage unless the only way of not taking it would be to waste too much time (I consider even 1 second to be too much).
As for taking damage on purpose in other places, do you have anything concrete on mind? I'm not aware of any place where I could have saved time by taking damage.
And as I said earlier, you can't control the frequency of the items. Even if taking damage would speed up something, you can't get the bottles whenever you like.
8 stars is a must in the timeattack, 3 for the "power up" and 5 for the "attack & assail". You can get a total of about 10 or 11 items in the timeattack, but you really don't have time for more.
For those who don't know:
Rygar can cast three types of magic: Power up, attack&assail, and recover.
"Power up" takes three mind points (which you get with the stars, that is, you need to collect three stars in order to cast this spell). You can cast it only once, but it lasts for as long as you are alive. It makes your hits stronger and your shield to reach farther. For this reason it's very important to get three stars as early as possible, definitely before the first boss (the forest monster). Once you get it, you have this boostup for the rest of the run. (And as I said, you can only cast it once, so you don't get any additional boostup by casting it again later.)
"Attack & assail" gives you 10 hits to every monster in the screen and it consumes 5 mind points (meaning you need to collect 5 stars). Even though this would be handy for all the bosses, you simply don't have the time to collect the required stars. In the timeattack I reserve this spell for the final boss, which is the most difficult one.
10) It's usually unnecessary, and I didn't do it in my first nor second timeattack, but I had to curse the entire family of that **** boss because no matter what I did (and I even tried to play that entire level leading to that boss again) this time it shot two of those fire thingies right at the beginning. I certainly tried everything I could to avoid them without losing time, but for no avail. What you see in the video is the *only* and *fastest* way of avoinding them which I could find. Honestly.
