Glad to hear you are enjoying Troves!
1 - "An Ability can be used at any time as long as the rules listed for the ability make sense..." (p. 7). No need to declare using Stamina before it is needed!
2 - Correct; All HP (and 1 Stamina) is restored after a successful Combat (p. 27). This was done to prevent softlocking of progress for players that don't have healing options (Trials only deal 1 Harm for failing them, see p. 26).