Congratulations! Definitely sounds like your incubator is running a bit cold; next time you hatch, you can nudge it up a degree and see if they pop out sooner. :)
Sounds like the chicks have spoken, they like the new plate! Your set up sounds good now that the defective plate is out, so good luck to you and your chicks.
Just give them a for bath and use your nails to break it off in stages. Gross but effective. And then, of course, fix whatever in your cage is causing it!
I'll weigh in as someone who does use heat plates and likes them: the exact temp under it doesn't matter as much (since they work differently than heat lights), the behavior of the chicks do.
Chicks that are under and sleeping quietly are happy warm chicks; chicks that are peeping a lot are too...
If you have extra boys and don't need him, I'd cull. If you do want to keep him, I had success with a broken legged hen a few months back--I moved her to her own little enclosure (a spare Rubbermaid) and set up water, food, and calcium where she should reach all by just stretching out her neck...
There is DEFINITELY variation, I'm also at 2/3rds the expected eggs, and mine stopped laying entirely when I tried to just use Christmas lights. Had to give them a big bright floor lamp before they got back in gear. Another thing to add to the breeding wish list!
I don't know about your kiddo, but mine got over it real quick once he tasted his first quail, lol. Now whenever new boys start crowing he asks for "quail eggs and quail legs" for dinner!