In regards to the fans, I suggest you get some monitoring software to check the temperatures. The fans will only run more, and more loudly, if either the device is overheating, or the fans are in need of cleaning, repair or replacement. So I would start with the monitoring to get a better idea.
Since this is a used device you don't know how dirty it may be inside (dust, debris, who knows what else) which would make the fans have trouble running correctly. It is also possible that they need repasting (thermal paste) or even the fans replaced. If you feel comfortable doing all that yourself, great. If not, then I would try a local tech.
As for the broken part, depending on the location of the damage and how extensive it is, there may be nothing to do to repair it other than replace parts. When you take the laptop to a tech to look at the other issue, they can give you a better idea of this fix as well.