As of stealth, this is a rogue only thing.
This requires the talent "Subterfuge" which basicly grants 3 extra seconds of stealth.
But, with the talent picked, if you start to cast a mount, Subterfuge doesn't pop, which is intended to bring you out of stealth after 3 seconds.
This also works with the Hearthstone, so you can hearth while stealthed, and land at your HS location while in stealth.
It is intended to break stealth when starting to use items (but poisons). Stealth broke on the start of mount cast with the 2 other talents.
Havn't tested with more items, as my rogue don't have any more items.
Thanks Caroarcus.
Can't provide a pic with the HS yet (damn lvl 1 guild bank).
Sorry if a repost, search didn't bring anything up (keywords: Subterfuge, cast in stealth)