To have a phoenix, you must have a good alignment. You will find it randomly in the forest.
To get a horcrux you have to be evil (at least -50 alignment) and get 5 player kills. They will resurrect you when you die, it will not grant you a new day.
More information about phoenixes and horcruxes are found in their respective section in the FAQs.
Some pets can help you in battle, you can order them to attack to help defeat creatures when you're in trouble.