Reading roots is an artform, but you can get some clues from the form of the trunk where it buttresses, and bulges in the ground. Further clues from the shape of the canopy. As a general rule of thumb, primary roots (the big ones) will usually extend out to the drip zone (the limits of the branches) though it can be further with some species, but rarely less. Taller narrow trees like poplars for example, will extend out beyond the drip zone, but for most spreading canopy trees expecting primaries out to the drip zone is a fair rule. Secondary roots can extend out up to 10x the drip zone, but are unlikely to do anything or even be noticeable.
The question of whether cutting branches back will prevent root grown is an interesting one, and my best guess would be that it probably does, but not to the extent that you're hoping. Restricting root growth does seriously prevent tree growth though. You can't just go hacking away at roots at this late stage in the game, they're holding the tree up. You will get much better advice with pics.
Shaun