Oh, regarding the burned spot, if the coil failed because it picked up lint, that burned on, insulated/heated up more from the lint catching fire/whatever, bending the coil outwards could actually make it more likely to catch lint/whatever. No idea with your dryer if that chance is better or worse than the possible benefits of spreading, just a thought.
Some greases are incompatible, and not cleaning thoroughly causes them to react chemically and cause issue, but unless you’re in that situation, you don’t need to clean super well.
While there is a certain level of innate technical mindedness that people have… Being willing to try to fix it, and the lessons you’ll learn from either fixing it or not is huge. Regardless of outcome hopefully the experience will be somewhat fun and pay dividends in terms of being able to recognize where vacuums get bound up with clogs, hair, etc. Occasional deep cleaning will make all the vacuums in your future live longer and suck harder.
Projects that are ‘either it gets fixed or tossed’ are great, there’s so little pressure, and so much you can learn.
Feel free to ask more specific questions if you get deep inside it and come up with them!