I Love this. I got the original watch as a gift in 1989 and played it a ton. Unfortunately I lost it a couple years later and always wanted to be able to replay it in a more convenient way. I was working on the same game myself in GB Studio but since you've already done a great job, I can switch to a new project, lol. I have plenty of notes and resources from when I was working on my version and I'm happy to share with you to help you make a definitive version. I have numbered my answers below to your questions you have listed. I'd be happy to help further if you need it. Let me know and I look forward to playing the complete version.
1. <BOMB> You just have to be more than 1 space away from the front of the stand the dragon is on (basically you need to be away from the spot where you place the bomb). I always moved to the lower right corner since it also kept you out of range of the fireballs as well. Also, the bomb is supposed to appear soon as the dragon appears instead of a delay.
2. <HEARTS> The hearts are supposed to show up starting on the 3rd and 4th room of each dungeon. When you collect more than 3, you should get another shield and that new life will set you back to 2 hearts each time.
3. <ENEMY MOVEMENT> I think it's tied to movement and timing. You can move past enemies if fast but if there's any delay, you take a hit. Basically, if something is next to you for a whole second, you take a hit.
4. <ATTACK> Your current approach is correct. You can attack from the right or left.
5. <ENEMY MOVEMENT> As far as I know, it's always been random at all times. I think more complicated enemy movement "AI" was beyond the means of these kinds of simple LCD Games. Your current approach feels correct.
6. <DEATH/GAME OVER> Yes, your current set up seems to be correct. 0 Hearts = -1 Life, 0 Lives = Game Over