About the ghb quests

Myrrh makes flying quests easy. Especially once she gets DC since she can bait, counter attack, and murder most units.

I think a good investment for your team would be a Galeforce Cordelia.

It really depends on the Map and the units you have. I'm guessing a lot of your challenge comes from the units. Good thing is that Lance Fliers are probably the most common type so finishing out the triangle should be rather easy. Just figure out what kind of role you need filled (Type Slayer, Tank, etc.) and choose/build the unit from there.

I find flyer emblem to be super easy as long as you have one blade tome mage (I use summer Corrin) and one dancer. Corrin runs double Savage Blow to soften up stat inflated enemies.

Some of the maps are extremely hard if you don't have two dancers or a solid enemy phase unit who will survive multiple hits.