You can chalk Erza getting back up to POF, and it's true that Erza is better at using POF than Mirajane. That's also why she's stronger.
And actually, the Tenrou Tree technically provided Erza with more buffs than it did to Mirjanae. The tree gave 2 buffs. One was divine protection from death, and the other was a boost to magical power. When the tree was down, it only gave Erza the divine protection from death. The boost to magical power only came into play after Ultear restored the tree.
Irrelevant. Mirajane considered using all her power to fight Azuma, and simply decided she wasn't strong enough to beat him. Also Mirajane barely did any damage to Azuma, other than few superficial scratches. He was in near optimal shape walking away from the fight, and also in near optimal shape when he began the fight with Erza. Saying that Mirajane did this amount of minute damage to him in 2 minutes doesn't say much.
She said, "I can't, he's too strong", and then considered her chances of beating him if she used all her power. Then decided that she wasn't strong enough to beat him, and admitted it. She then (probably) used her remaining power to protect Lisanna.
She also said earlier that she didn't think her magic would last very long.