what does it mean to have made "partner" in a firm, a percentage of the cases won, or of the company......??

Answer 1

It is different with every law firm. Typically, there is a progression from Associate attorney to Senior Partner.
The Associate is simply an attorney that works for the firm. If he/she works very hard, they can move up the path to become a senior associate. They will then bill out at a higher rate and of course collect a higer salary.

The owners, or partners/senior partners will select other partners from the senior associate ranks.

In short, if you can collect a lot of fees for the company and are a politically viable attorney, you can be promoted to the partner level. Of course, politically viable means something different with every firm. 60 hour weeks and winning cases/motions is the surest path to partner.