rēx Sāturnus tantā iūstitiā
This is what Allen & Greenough call "descriptive ablative or ablative of qualify" (sec. 415).
more literally, "...is said to have been with such great justice..."
This construction is usually translated using the English preposition "of": "is said to have been [a man] of such great justice"
With regard to your larger question, I think you have to read enough so that you internalize the rules, and don't have to think about a particular rule each time you encounter an instance of it. You have to force yourself to do this at first. Eventually, if you read enough, you will get there. (I find, though, that especially with ancient languages, there are always passages that stump me, and that I have to think about in terms of grammatical analysis. Sometimes I'm gratified, however, to find out in annotations that the analysis of these passages is disputed.)
Unfortunately, the best Latin author for assimilating the variety of constructions that Latin is capable of in a relatively simple style is Caesar, who seems to have been banished from the first and second-year classroom because he's so boring. But if you hack your way through Caesar for a while, you can pick up the ability to read naturally, without focusing on every point of syntax.
I would also recommend reading Cicero, Livy and Tacitus. Reading Latin poetry is a somewhat specialized skill, but once you acquire it (it involves tricks like anticipating that the noun at the caesura will be modified by an adjective at the end of the verse, for example), I think, Vergil and Ovid, and even Horace and Catullus, are actually easier than many prose writers. Ovid is dazzling and often outrageously funny. Everyone has their favorites, though.
I would also recommend getting beyond made-up Latin as quickly as possible and engaging with works written by native speakers. You should equip yourself whenever possible with good commentaries which can not only help with understanding the grammar but also the background of the texts.
Those are some thoughts of my own. I'm not a professional, but I started studying Latin in 1958 when I was 12, studied it through high school, majored in Classics in college, and have been engaged with the language throughout my adult life.