QCan I only play this spell when I can select both an Armed follower on my field and an enemy follower on the field?

AYes, that's correct.

QIf I put a follower into the EX area with this spell, does it lose any damage dealt or abilities given to it?

AYes, it does.

QIf the EX area of the first follower's owner is full, does it still get moved there?

ANo, it remains on your field.

QWhen playing Armor Burst, if I select a Lance Lizard on my field and an enemy Goblin, what happens with Lance Lizard?

AFirst, you resolve Armor Burst, which puts the Lance Lizard into its owner's EX area. Then, you resolve Lance Lizard's ability, which triggered when you selected it with Armor Burst. The effect "give it +1 attack" refers to Lance Lizard as it was on your field when the ability triggered, so now that it's in the EX area, it doesn't gain the buff. However, you still deal 1 damage to each enemy leader.

QIf I can't select an Armed follower on my field, can I still select an enemy follower on the field and deal it damage?

ANo. If you can't select an Armed follower on your field, you can't play this spell.