Ok, so there are parts that can be solved through a good communication with your dentist.
You migh agree to give you few short breaks during the procedure so that you can relax a bit. I know that rubber dam can be taken of too if you need a break so it might be worthy to discuss this with your dentist. It is all about letting him know and about his flexibility. We had a post here on the forum few weeks ago with a user asking wether taking breaks during a root canal would be possible and the answer was yes, so you might ask your dentist and make sure you get some breather. I will see if I can find the thread.
If keeping your mouth open for a long time bothers you, you dentist might suggest using a biting block which is something you can bite on for your jaws to feel more comfortable. Again, if you let your dentist know, he might show it to you and see if you like it or offer you other ideas.
Swallowing and bleach taste should not be too much of a problem as you will have the rubber dam which isolates you from that. Again, letting your dentist know will help him to be more careful. The bleach dentists use is the same thing that gets used for swimming pools so if you are worried about the smell and open to ways to overcome it, you might consider going to a pool to get used to that smell.
Breathing is a huge one, I understand you are worried about this. This has a lot to do with self control and being confident that you can breathe. You could train this / test it out if you like - by laying down and testing around a bit - can you breathe comfortably while being lied down? Can you breathe through your nose comfortably while having your mouth opened? You could also try to cover your opened mouth with your hand and see if you can still breathe through your nose comfortably. Once you experienced this being possible, you will feel much more confident for a treatment. You cannot imagine how much time I had spent lying on the floor with my mouth opened imagining a dental treatment in order to desensitize myself. It feels a bit silly and you want to make sure nobody sees you like that but it helps
Last piece of advice is breathing. There is a trick I learned from Dr.Mike Gow who is one of the dental superstars here. You would breathe in on 4, hold your breath on 4 and breathe out veeeeeeery slowly on 8. This is my holy grail when it comes to fighting any anxiety or nervousness and I use it every time I get uncomfortable. If you like to try it out, start using in during the day any time you feel nervous so that it gets natural. There are of course a lot of other techniques out there to calm yourself down so take whatever you prefer.
These are just some suggestions, as always, everyone is different so some things might work for you and some not. Let us know how you were doing and if you find a good strategy to deal with the treatment, make sure to share
All the best wishes