Front strut replacement instructions ?

In the picture I've attached you can see the two cracked pieces on my suspension. I am looking at having a local garage fix it, but I would like to buy the parts myself beforehand. Could someone help me identify what these are and approximately how much I'm looking at to fix it?

I found out about the issue when out of nowhere I experienced a horrendous shake in the rear passenger side and did some investigation.

Also, is it safe to continue to drive on this? If so, how far? I've heard from a couple of friends that I can, but they are by no means professionals.

Thanks!