If I empowered a Steel Paws, and I play a new Steel Paws, does the other Steel Paws get empowered too?

No, playing a new Steel Paws does not empower an existing Steel Paws.

Each Steel Paws must be empowered individually by paying its Empower [7] cost. The Empowered keyword just grants a continuous +7 Might while the unit is already empowered — it doesn't trigger off other units being played. There's no text on Steel Paws that says anything like "when you play another Steel Paws, empower this unit."

So if you have an empowered Steel Paws (at 7 Might) and play a second one from hand, that new one enters at 0 Might and, unless you also pay Empower [7] on it separately, stays at 0.