For the OP, you can target yourself and hit enter. That will bring up the hotbar.
As for chat box, in Phase 3, nearly every piece of UI was moveable (it forgot once you logged out) and the chat box was completely resizeable. It would be safe to assume that this was probably intentional, and that your positioning will be saved once the game is released (or even in open next week). I did say assume though, so that could find me 100% wrong. ;)
FFXI: Edalya, Valefor Server 99WAR/99PLD/99DNC/75DRG (Retired)
FFXIV: Edalya Evenstar, Excalibur Server 46DRG