Name and Value of This Mower?
Its a (Jacobson ) obviously, greens mower for golf courses. I learned to mow greens with one very similar but not as old.
Value of Eclipse Push Mower?
If you know someone that works on a golf course or any kind of nice ballfield they can probably help you sharpen it with a backlapping machine if they are cool.
Sharpening a Reel Mower?
Its called back lapping. There are tools and machines that spin the real backwards and you brush back lapping compound on the real while its spinning or go the cheap rout and use sand and old motor oil.