Transient and Steady-State Response

Almost every time-domain question reduces to matching $\omega_n$ and $\zeta$ from the characteristic equation $s^2+2\zeta\omega_ns+\omega_n^2$, then reading off the formula you need. Poles sit at $-\zeta\omega_n\pm j\omega_d$: the real part sets the decay, the imaginary part the ringing.

Type = number of poles at the origin in the open-loop $G(s)H(s)$; order = degree of the denominator. They are different things and the question always means type. A type-$N$ system tracks inputs up to $t^{N-1}$ with zero error and the $t^{N}$

A pole five times further left than another contributes a term that has decayed to nothing before the slow one has moved, so the response is effectively second order. This is what lets the formulas above be applied to higher-order systems.