Nice work so far. I think you are saving money. I'd do the #3 coil and hold off on the injector if you can return that for $ later. Did you put some new spark plugs in there? It would be a good time. There's coincidentally a YouTube video (maybe you've already found it) that uses your car as an example and discusses replacing the coil. Here's a link to that. Now, I've had similar in my 240sx and for me it was a fuel injector getting stuck part time. But, I did not get the P0303 code, so I think you're on the right path. The mechanic place with the high quote was just covering all the options and being up front about the cost, so I think they were doing a good job and being legit. I'd consider using them again in the future when the work gets beyond your abilities.
Clearing the fuel line is to keep you from getting doused with gas while working. You'll be fine if your not a smoker. If you are, be careful with the matches!
As far as the rubber bit, I'm guessing distributor plug wire parts, valve cover gasket or gobs of liquid gasket, but I don't know. Clean up the loose bits and replace your seals as needed.
https://www.youtube.com/watch?v=pP0I-iSBUF4
Finally, welcome to NICO Club!