OOC
I play a Lightfoot Halfling Rogue in another game, so I can help out with those kinds of questions. I had to contend with them myself. ^^;
Normally you can only move through an enemy creature's space if it's two size categories larger than you are. So, for example, other Small-sized Beings could only move through a Large or greater creature's space without being blocked by them. A Halfling's racial ability ignores this limitation and allows you to move through any size creature's space so long as they're bigger than you - so Medium and up. It does not, however, mitigate the "difficult terrain" situation, so you still move at half-speed even through an allied creature's square to represent shuffling past them.
As for the "Naturally Stealthy" ability, you can hide behind a creature that's larger than you are (so Odette is the perfect obscuring feature there). You reveal yourself as soon as you make your attack, though generally speaking it's assumed a Rogue would time their moment to strike so as to actually get the benefit of being Hidden, otherwise the mechanic is kind of pointless. Leaping out to make a strike would generally not negate being Hidden, though if you had to move a significant amount of space through open terrain, that would allow the enemies a chance to spot you with a Perception check.
As for Advantage from being Hidden, it goes onto the first attack you make, so it'd be on your main hand attack.