I'm new to the game, and these questions have likely been asked, but not by me.

FIRST: Solitaire game state is Threat Level 29; Hummerhorns UN-ENGAGED up in the staging area (threat rating 40, damage 3); Core Set Gandalf in my hand; 5 resource tokens on 3 heroes; I'm in Planning Phase.

I'll summon in Gandalf as an ally, burning the 5 resource tokens. "After Gandalf enters play..". can he use his "deal 4 damage to one enemy in play" as his response to blow the un-engaged Hummerhorns into next week and claim the victory points?

Put more broadly, is something that is in the staging area but un-engaged "in play"? I would think it is "in play" becoz it has a shadow rating that affects questing and is therefore involved in game play, but I'm just not sure that the Hummerhorn in this case can be victimized since he's not engaged -- it just doesn't feel right.

SECOND: Thalin has A Dwarven Axe, which gives him +2 attack. While he's questing, an enemy is revealed from the encounter deck. Does Thalin whack this enemy for 3 points damage becoz he can, or just 1 as his card explicitly states?

Put another way, is "deal[ing] 1 damage to each enemy as it is revealed by the encounter deck" the same as attacking that enemy, which would enable the +2 Axe attack bonus? My hunch is "NO", becoz if attack was meant, the card would have said "attack" instead of "deal 1 damage" and he'd also be invited to "deal 2 damage" becoz that's his attack rating -- BUTTTTT, if he can deal 1, why can't he deal 3 with his Axe?

Your hunches are correct.

"In play" means that the card is on the table, and not in your hand, in the encounter deck, in a discard pile, etc. Gandalf can put damage on any enemy in play regardless of whether they are engaged with (any) player or in the staging area.

Thalin's effect puts only 1 damage on enemies revealed from the deck. The axe's bonus only comes into play during an "attack," which means a declared attack, normally during the combat phase (but can happen outside of the combat phase, e.g. if you use Quick Strike).

Enemies that are in the staging area are "in play" and hence are eligible for Gandalf to deal four damage to. The only exception would be an encounter card that says it's immune to player card effects.

Regarding Thalin: his response is passive and is not an attack. So even if he is has a dwarven axe or some other attachment that increases his attack strength, he will still only deal one damage to an enemy when it's revealed.

Thanks! Thats what I thought on both questions, but its good to get confirmation.