To confirm with others: My halflings are "small", averaging jsut under 3 feet tall. Most other humanoids - humans, elves, half-elves, tieflings etc., are "medium" sized creatures.
In 5e, ANY creature can move through the space of a hostile creature if that creature is at elast 2 sizes larger or smaller than them (so a Dwarf (medium), can move through the spaces occupied by a Balor (Huge), treating those squeares as difficult terrain).
Halflings have a special racial trait that specifically reduces this to 1 size category - meaning that halflings specifically can move through the spaces of any medium sized creature, which is most humanoids. Moving through their space will count as difficult terrain, but they very much should be able to do it.
Yep.
Not even a personal guess on what halflings "should" be able to do, but as Niara is pointing out an explicit part of the rules.