I suggest that you rule out an intermittent alternator. The symptoms could be quite similar, and would most likely be caused by failing brushes, which intermittently make contact with the slip rings. Another common failure mode is that a overrunning clutch on the alternator intermittently grabs and then releases, which results in a period of intermittent ...
Answers to your 3 questions:
1) No, there is no such "magical" device. If there were, everyone else would know about it too. When a battery is past the end of its service life there is no process to revive it.
2) Moot question in light of the first question.
3) I'm going to speculate that the initial test was faulty. The dealer likely charged the ...
I had a 1990 Honda Accord that had a very similar problem. It would often make a squealing/whirring noise when turning at intersections. The noise sounded like it was coming from the other side of the dashboard, near the power steering components.
I finally checked, and the power steering fluid was low. Filled it up to the correct level with the proper ...
No magical devices to bring a battery back to life.... except water if the level in low.
Based on my experiences with dealers, a crooked service tech told her a good battery needed to be replaced. During the visits later on, you got an honest tech.
Go to a website advertising cars for sale. Locate some dealers in your are selling Honda Fits with a year similar to your vehicle. Go to the dealers and test drive these Fits to get an idea of what the normal clutch pedal feels like.
The most probable reason for the engine not to start after a coolant loss is a compression loss due to overheating. High temperature causes a (usually) aluminium cylinder head to bend and lose a good airtight contact with an engine block.
I'd start with a compression check, it won't cost you much.