1. Yes, they are. They're very useful for certain things. For example, want to update your fulltext index in Postgres after certain table cells change or when new rows are inserted? You'll need to use a trigger.
2. Knowing more rather than less is probably a good thing. Understanding the underlying model of relational data will help you build SQL databases that make sense given the data you're working with.
Of course, you won't use SQL in every project or job, but it's awfully useful. Ignore the hype that NoSQL is the wave of the future. It may be a wave of the future but so is SQL.
Are SQL triggers still relevant? How much relational algebra do you really need to know? I think I've used this stuff maybe once since then.