This gets asked a lot and I've answered it a lot, too. So don't mind me just shortening it to the bullet points. A lot of this stuff was answered on the official forums and by Koji Fox during early Dev Lore Panels a number of years back and is amended to include additional details provided in-game.
They can crossbreed.
Lalafells and Roegs are different branches of the same immediate "human" species of FFXIV (so you might consider it equivalent to European descent versus Asian descent yet still all being Homo sapiens sapiens). Keep in mind that racial Garleans are their own separate branch of the Lalafell/Roeg/Hyur/Etc. racial lines as well--the actual army is a conscript army of conquered lands and only people like Zenos, Cid, or Nero represent the racial Garleans. That all said, successful crossbreeding in general is apparently rare.
It's generally a bit of a social taboo to engage in mixed breeding so it isn't common.
Though obviously nobody seems to give a damn about sexual relationships, it's actually having children that society at large gets a bit iffy about the matter.
The mother dictates the primary physiology of the child.
Prevents the Aliens chest bursting issue for the smaller races mixing with a larger race.
The father affects secondary characteristics.
So in the case of an Au Ra mother/Hyur father (example provided in-game), the children were all Au Ra in overall physiology but featured unusually sparse scale density and I believe also shorter tails compared to full Au Ra.
True hybrids are exceptionally rare.
The only known example in-game is Hilda in Ishgard that is a true Hyur/Elezen hybrid rather than being a Hyur with minor Elezen characteristics or Elezen with minor Hyur characteristics. Otherwise you'd normally get an Elezen featuring short ears and relatively short stature or a Hyur that was relatively tall with maybe oversized ears or longer limbs or something.
And regards to #5 especially, given the hilariously massive amount of...intermingling between Hyurs and Elezen in Ishgard, Hilda is basically something that just doesn't happen. She's such a rarity that in the plot she's even identified specifically by the fact that she's a hybrid and not merely one-or-the-other exhibiting a few traits. Hilda the Mongrel, as it were.
https://www.reddit.com/r/ffxiv/comme...erent_species/