For #2 I believe the answer is no, because when they are knocked out there are just a token not a hero until they are stood up.
The rules say you remove your figure - but your hero is still on the board as a token.
D2E Rules page 15 wrote:
When a hero is defeated [...] the controlling player removes his figure from the map, replacing it with one of his hero tokens.
A space containing a knocked out hero (represented by a hero token) is considered to be empty to other figures for the purposes of movement. In other words, any figure may move through and end its movement in that space. Also, knocked out heroes do not block line of sight.
But then there is this part.
A knocked out hero cannot receive any Condition cards and is immune to all attacks and most hero abilities.
That might mean you can't OoH to them, but OoH doesn't effect the chosen hero so maybe it doesn't violate "immunity".
I hope you can. Thematically the hero is still in that space, just knocked out, and what better way to observe an Oath of Honor than to aid your fallen comrade?