You can choose not to copy anything. In that case, Phyrexian Metamorph simply enters as a 0/0 artifact creature and is put into its owner's graveyard as a state-based action (unless something else is raising its toughness).

If the chosen permanent has in its mana cost (such as Protean Hydra), X is considered to be zero.

If the chosen creature is copying something else (for example, if the chosen creature is a Clone), then your Phyrexian Metamorph enters as whatever the chosen creature copied, except it's also an artifact.

If you're at 1 life or less, you can't pay 2 life.

Except for also being an artifact, Phyrexian Metamorph copies exactly what was printed on the original permanent and nothing more (unless that creature is itself copying something or is a token; see below). It doesn't copy whether that permanent is tapped or untapped, whether it has any counters on it or Auras attached to it, or any noncopy effects that have changed its power, toughness, types, color, and so on.

A card with Phyrexian mana symbols in its mana cost is each color that appears in that mana cost, regardless of how that cost may have been paid.

To calculate the mana value of a card with Phyrexian mana symbols in its cost, count each Phyrexian mana symbol as 1.

Phyrexian mana is not a new color. Players can't produce Phyrexian mana.

As you cast a spell or activate an activated ability with one or more Phyrexian mana symbols in its cost, you choose how to pay for each Phyrexian mana symbol at the same time you would choose modes or choose a value for X.

If Phyrexian Metamorph copies a noncreature artifact, it is no longer a creature.

If Phyrexian Metamorph somehow enters at the same time as another permanent (due to Mass Polymorph or Liliana Vess's third ability, for example), Phyrexian Metamorph can't become a copy of that permanent. You may choose only a permanent that's already on the battlefield.

Any "enters" abilities of the copied permanent will trigger when Phyrexian Metamorph enters. Any "as [this] enters" or "[this] enters with" abilities of the chosen permanent will also work.

If the chosen permanent is a token, Phyrexian Metamorph copies the original characteristics of that token as stated by the effect that put the token onto the battlefield, except it's also an artifact. Phyrexian Metamorph is not a token.