xxxxxx I had Apprentice Magician in face up attack position. I attacked and activated Magician's Circle and brought out Hand of Nephyts. Can I Special Summon Sacred Phoenix during the battle phase and attack?

No...you can only activate Hand of Nephthys's effect during your Main Phase 1 or 2...

Ignition effects are always Spell Speed 1. You could pull out a Neph but not until MP2 as HalfDemonInuyas said.