For me, if I was experiencing a db error I would not ask my host if the db was working until after I did my homework.
Log into your website or domain admin. Go to HostManager or the like or look around until you find something that says database. Go there and you should find a database admin which is often myphpAdmin but whatever it is you should be able to log in. The name and password you use to login with is what goes into the wp-config file.
After you have logged in your db admin should say somewhere the version of mySQL and “running on XXXXXXX” That most of the time (maybe not 99%) will say local host but whatever it says is what you put into your wp-config.
While you are there look around. Open some screens and become a little more familiar with the “heart” of WordPress. Just DON’T change anything. When finished log out.
If you cannot log into your database neither can WordPress. As clussman9 said shared db can cause problems but AFAIK nomally only a slowdown. If someone is crashing the db the host won’t put up with that for long.
If you are tracking errors great! When the db goes down, call the hosting company and tell them it is down right now. Send them screen shots. That will help them and they will fix it or move you to a better database (I know from experience).
Finally (yes, there is an ending) if all has been running ok and then suddenly changes and you have done nothing then it is the hosts problem not WP. Something has changed on the server. When you log into your website admin you should be able to find server information somewhere. Print that out. If suddenly you have a problem go to server information and compare.
People won’t do it for you. You have to be a sleuth to open the doors so your host will look in.