I'd go ahead and replace the plug...it's only a few bucks
I'm guessing this is electric start? The red is ignition on/off and yellow button should be to engage the starter.
I soak my air filter in a coffee can with dish soap...works great. I'd try to straighten the air filter as best you can....I've seen worse. And yes if you have the K&N filter cleaning kit you can use it with that filter.
Cant tell how well you cleaned the carb but I circled in red what is most important. I have the same carb, when I have time I will post pics on how to clean it very well if you need me to.
Be sure to remove the float and jet and make sure it's not plugged in their. From the looks of the float it sat with gas in there for a while and a good chance it has gummed up in their
The best way to clean the carb is to take it completey apart and run down to local auto parts store and get a can of parts &carb clean solution(not the spray type) and put it in a cofee can and soak it over night.