Can I use Necromantic Summons on Gaea's Revenge in a graveyard, or does the "cannot be targeted by non-green spells or abilities" effect kick into play?

In the same way, can Thoughtseize hit Gaea's Revenge?

Yes to both

Say I have a Sylvan Advocate on the board and six lands on the battlefield, one of which is an Evolving Wilds. The Advocate has taken four damage. If I sacrifice Evolving Wilds, does the Advocate die during the phase when I only have five lands on the field?

Yes!

Yes.

Yes because its toughnes becomes low enough to kill it

Was hoping Evolving Wilds leaving the battlefield and the new land coming in would be "instantaneous" so Sylvan Advocate survives, but I guess not.

If I put a +1/+1 counter on Kytheon and then it flips, will it still have the +1/+1 counter when animated?

No because he doesn't just flip, he leaves the battlefield and comes back transformed. Though if you activate his human ability whilst he is a planeswalker then he will keep +1/+1 counters you put on him at that time for the next time you activate the human ability (assuming he isn't somehow removed and replayed as Kytheon again).

Thanks. I was going to ask if +1/+1 counters worked if put on something that transforms like Lone Rider, but then I remembered I've seen that interaction before in the game and the answer is "yes".

If I do one damage to a Woodland Wanderer, can I hit it with Gilt-Leaf Winnower? I really don't know about this one. I imagine the answer is"yes" since at that point the Woodland Wanderer shows up with unequal power and toughness, but maybe it's still treated as having equal power and toughness, it's just damaged.

EDIT: Also if I use Liliana, the Last Hope's +1 on that Woodland Wanderer, I should be able to hit it with Gilt-Leaf Winnower, yes?

Damage doesn't change the base stats of a creature, that's just the way Duels represents damage that has been done, so Gilt-Leaf Winnower still can't hit Woodland Wanderer. Lilly does change the stats, so yes in that case you should use the Winnower there.

Renegade's Getaway
Card Text: Target permanent gains indestructible until end of turn.

Can you target a PW that is being attacked/burned to save loyalty counters?

I don't think it works that way, the planewalker would still lose all its loyalty and then be put in the graveyard as i don't think having 0 loyalty counts as a destroy effect

If my lands get Deep-Fiended in upkeep phase (which I would have thanks to Lifecrafter's Bestiary) and in response I float my mana, can I play sorcery speed spells in my first main phase or does the floating mana disappear after my draw step?

Mana would dissapear as you change from upkeep --> main phase

Correct - any damage to the planeswalker will still remove loyalty counters, and if it reaches 0, it is placed in the graveyard next time state-based are checked.

This is why Gideons +1 ability is worded with both indestructability and prevent all damage.

No, the mana pool would deplete once you hit your main phase.

That's the main reason why EDF is so good in general.

Here's another Dummy question:

If I'm resurrecting two creatures with my Ever After they become zombies. But do they stay Zombies when they die again? In other words, will the two creatures stay targets to get them back again with Cruel Revival?

I think they are only zombies while on the battlefield, the altered creature type will not stay once they die again.

Shouldn't Kytheon transform when he attacks together with Kari Zev? He didn't when I tried it.

"Kytheon’s first ability will count creatures that attacked but are no longer on the battlefield (perhaps because they didn’t survive combat damage being dealt). It will not count any creatures that were put onto the battlefield attacking, as those creatures were never declared as attackers."

so no, he will not transform

Gatherer rulings are your friend