From the Player's Basic Rules, page 71 (or PHB p. 191):
In contrast, you can move through a hostile creature's space only if the creature is two sizes larger or two sizes smaller than you.
An ogre is a large creature and elves are medium. So an ogre can't move through an elf's space. In your previous example, if we have a 10-foot wide passageway with two elves standing side by side, the ogre can't get through without killing one of the elves or forcing them to move.
The rules on squeezing into a smaller space are for an ogre trying to move along a 5 foot corridor. The rules on creature size that you've quoted back this up—the ogre isn't actually 10 feet wide, that's just the space he controls. So he can move through a 5 foot wide gap, but it's cramped and he can't move freely.
Now, you might be thinking that it's a bit unfair on the ogre if the 2 elves can form an impenetrable barrier against it. As you've said, he'd rather shove them aside than squeeze between them. And he can do just that! From the Player's Basic Rules, page 74:
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
The target of your shove must be no more than one size larger than you, and it must be within your reach. You must make a Strength(Athletics) check contested by the target's Strength(Athletics) or Dexterity(Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you.
So you're right, shoving is the ogre's answer here.
Now, with your new example, (2 elves in a 15 foot corridor with a 5 foot gape between them), things are different. The ogre does indeed have to squeeze between them. Fortunately for him, it's not going to matter all that much.
Why? Because he's almost guaranteed to be moving on his own turn. Unless there are more enemies than just the elves, he's not going to provoke any opportunity attacks while squeezing, and he can attack before or after he squeezes. So the only squeezing penalty that is actually going to apply to him in this situation is the double cost for movement.
Note that if he stopped between the elves, all these penalties would apply to him. That makes sense though—standing between two enemies with not enough space to move around in would make it difficult to dodge attacks or attack effectively.
Yes
You are reading this correctly. There is no saving throw if the subject is within the up to 20 ft/side area the cage appears to surround. Besides high level magic, shrinking or turning gaseous or whatnot(if the cage version), spells on the caster (if the cage version), you're looking at an hour of sitting still.
Best Answer
There is no rule that applies any stricter carrying capacity for flying creatures, so you'd default to the standard carrying capacity on p.176 of the PHB.
Picking up and carrying a character would fall under push, drag or lift, so it would be 30 times the pteradon's Strength score, or 360 lbs. At that weight, the creature's speed is reduced to 5 ft. Below 180 lbs., it can move at its full speed.
According to the rules for flying creatures on p.191, a flying creature drops if its speed is reduced to 0 or if it's knocked prone. Since the pteradon in this case has a speed of at least 5 ft., it can still fly until it's carrying more than 360 lbs.
You can also apply the optional Encumbrance rules from p.176, which will reduce the pteradon's speed more incrementally, but the general rule remains that as long as it has Speed, it can fly.