1.) If I attack with a Morphling and my opp has 4 Caltrops in play, can I make the morph 5/1, do its damage, then pump it to a 1/5 before the damage/stack whatever resolves?
2.) If I have a Manabarb in play and cast a Mana Short on my opp, does he take X damage for his lands?
3.) Also with Manabarbs, I am not too keen on the "stack" but if I have 4 Manabarbs in play, and one Urza's Armor, whenever I tap a land, does each damage (one at a time not 4) go on the stack, then each damage is prevented by the Armor, making me take no damage?
1) No. Caltrops triggers when the creature is declared as an attacker. This effect will resolve before blockers are declared, and any effects that trigger then must resolve before combat damage is put on the stack. Morphling can't attack for more than 1 damage per turn with that many Caltrops in play.
Whenever a player taps a land for mana...
Tap all lands target player controls and empty his or her mana pool.
Mana Short causes the lands to become tapped but does not tap them for mana, so no damage happens. Drain Power works, though.
3) That works for the reason you stated - each Manabarbs generates a separate effect.