Need help in understanding the meaning behind the steps in a AL_iLQR paper

Question

I am trying to implement the AL-iLQR algorithm described in this tutorial. I am not familiar with the steps outlined in this paper and require some assistance in deciphering the notations under this particular section.

1. Under (5) does c(x) be either equality or inequality constraints? Or can it be inclusive of both?

2. Under (6) is Iµ a diagonal matrix consisting of the penalty terms?

3. Under (8) max(0, λi + mu c(x)) is this statement here to always result in non-negative numbers?

(https://bjack205.github.io/papers/AL_iLQR_Tutorial.pdf)