Identification of the system with zeros
Hint: It's a system with a damped oscillation of a single frequency sine wave, which also starts with an arbitrary phase. That should give you amplitude curve (damping), oscillation component (sinusoidal wave) and phase (starting point of the wave). If you can figure out the general form this system takes mathematically, it's a matter of plugging in the right values for those three.

Another hint:
Don't overthink the system order. Think about what a first order system could look like. Do you need to go further? What could a second order system look like? Do you need to go further, etc. I guarantee you will stop pretty early.

Perhaps a more important hint:
You're given a step response, not an impulse response, but there's a way to go from one to the other (what is it). Once you find the expression to describe this curve, going to impulse response should be very easy.

One last hint:
Depending on how your subject is taught, this may help or this may hinder your attempts, so take this one with a grain of salt. If it confuses you, ignore it. My Linear Systems professor said this and made us repeat this out loud in class almost every lecture: Solutions to linear systems are always exponentials!