I remember reading somewhere that Mike had reduced the regimes of Clemenza and Tessio obviously makin'a move out of weakness as it said.

1. How exactly was Mike reducing the strengths of the 2 regimes of the Capos (Captains)? Was he firing some of the Button Men that seemed useless to him? Or what?

2. Why was he makin' the move out of weakness? was it just to fool His rivals? Mainly Barzini? What's your take?

I think the novel says that Michael isn't reducing the size of their regimes, he's just not permitting them to recruit more men. And he's secretly letting Rocco build his own regime.
I believe Michael was not only feigning weakness to flush Barzini out into the open--he was also testing Tessio's and Clemenza's loyalty. He admonishes them to stick with him for a year, then they can either go with him to Nevada or form their own families. Obviously his "weakness test" worked in both cases.