专心 VS 专注 VS 关注, with 于 in the mix I'm struggling with a couple things...first is the ability to know when is the right time to use each of the above, each which seems to more or less mean "to concentrate on".

I think 关注 has the meaning more of like, following the news, updates, or something.

And I think 专心 is to concentrate in general, whereas 专注 might be to concentrate at the exclusion of other things... but I have no clue. And I'm struggling to figure out when you need 于 afterwards, and when you don't.
关注 has different meaning with 专心 and 专注. 关注 doesn't mean to
concentrate. Usually 关注 means to care about or to pay attention
to sth.
专心 and 专注 are very similar. They can be alternative to each other most of the time, although there are some collocations you can only use one of them.
As for 于, it is a preposition, same as on here. If you use 专心 or 专注 as a verb (usually a intransitive verb), then you may need it. 
Though 专心/注 can be verb, they are often used as adverb too. In such case, no more 于.
The (little) difference between 专心/注:


专心 is used more often to describe one's inner condition, while 专注 is used for one's appearance, look or expression.