First bomb can be avoided. You move too far to the left and completely move past the safe spot.
See here. You're lost somewhere in the blue box and wasting a bomb. The green box is safe.
Don't just grab whatever UFOs happen to pass by. Try to be more strategic about it and chain red UFOs or green UFOs to get you more resources, rather than simply grabbing what's there. Also remember that UFOs will linger onscreen for long periods of time, so you don't have to grab them right away. Take your time, pay attention to your UFO stock and think about if grabbing that UFO will actually help you, or if you should let it go. If it's a color changer, it may be at a more advantageous color when it bounces back toward you later on. If there is a UFO out, try to destroy it with normal fire before panic bombing; the UFO may explode, clearing the screen and saving you a bomb.
Kogasa's 1st: you didn't fail it, but I noticed you refused to move up from the bottom of the screen. Don't be afraid to move up if you see open space, because it may save you from getting walled (this is a general comment to apply anywhere in the series).
Kogasa's 2nd: actually, I'll say the same here: don't be afraid to move up. Especially in this case, where bullets come from the side and not from above, you're significantly better off staying in the middle rather than the bottom. Note that when you die, you can't move any lower because you've hit the bottom of the screen, and are forced into bullets above you. Had this situation occurred higher up, you wouldn't have been bound by the lower end of the screen and would have been safe by being able to move down.
Kogasa's 3rd: you're better off moving as the lasers stop rather than sitting still. If you're sitting still, you have to react to the laser stopping and move, by which time it's likely too late. Rather, as the lasers slow down, try to follow their movement with your own and stay inside the moving gap, if that makes sense. If nothing else, already being in motion gives your mind and your hand a bit of momentum with which to react when the lasers form, if you need to dodge them.
The Seizure Grid: this is a case where you may want to experiment with the idea that you don't have to hold the fire button down all the time. Rather, after summoning a UFO, try weakening it down to near-zero health, but then leave it alive for a bit, and destroy it when things feel too crowded. Of course, if it's too much to think about between dodging and firing and knowing when to stop firing and knowing when to start firing again and trying not to panicbomb, you may want to ignore this comment. Thinking too hard about it may compromise your natural dodging ability.
You die at one point chasing a UFO. Safety first. Don't put yourself in danger to collect resources. It's all for naught if you waste resources in the name of gathering resources.
Final section before Nue: this can be dodged, but I suck at explaining it. It's similar to the first comment I made, where you want to watch for that safe zone that unfolds a few taps away from where it's aimed. You can try following
this, but I admit that visually, it's not a very clean demonstration of the strategy. Feel free to bomb it in a real run, but if you get another run like this (where you enter Nue with a hopeless amount of resources), try dodging it and see what you come up with. It seems impossible until you do it once, and once you get it it's easy, and will save you a bomb if you can do it.
Red UFOs: remember when this card comes up in Nue's lineup, and remember to move to the right once it starts. First, make sure you don't get rammed by a UFO, then stream the bullets, move to the opposite side of the screen, and repeat. Hardest part of the card is remembering it's there and starting it correctly.
Ultimately, your biggest problem is confidence. You like to panicbomb. A lot. Touhou is a game of resource management, and while part of resource management is making sure that every bomb is used and you never die with them in stock, sometimes you have to trust in yourself to be able to survive something without a bomb so you can put that bomb to better use later.
I apologize if there's any errors in this post that cause what I say to make less sense. I'm lacking corrective lenses right now, and can't see my monitor very well, making it difficult to proofread.