SQL 2016 AlwaysOn Database Health Level Detection
If I restore a database, the state of the database will be RESTORING; will that trigger a failover event? 


No, because you can't restore a database that is in an AG. Thus, to restore it'd have to be out of the AG and wouldn't be subject to database level health detection.


  ... my understanding is that the database enters a Suspended state, which would make me expect the databases to failover as well.


Suspended isn't a database state - suspect is, not sure which you meant. Also, the key with this is that it may "attempt" to failover but doesn't mean it will be successful.


  So, is "Database Level Health Detection" only recommended if your cluster is only being used for one application?


It works at the Availability Group level, that's up to you on how and what you put into your AGs. You might have a single app in an AG or you might have multiple. Personally, I would only put the databases that need to be together in the same AG and not co-mingle any other application databases.


  For example, one of our clusters is going to host about 50 different databases used by our Intranet; if one of those databases needs to be restored or has corruption, I would not want the other 49 to have a fail over event and a small outage, or would that not be an issue? 


If your entire intranet relied on all 50 databases being on the same instance, then yes I'd put them all together... whether or not you want the AG to failover if a single database (might be the most important one or the least important one) has a state change. I can't make that business decision for you. I also can't change the need to have all 50 together.