Pack Rat's first ability counts any creature you control with the creature type Rat, not just Pack Rats. That ability works in all zones, not only the battlefield.

The token will copy Pack Rat's two abilities. Its power and toughness will be equal to the number of Rats you control (not the number of Rats you controlled when the token entered the battlefield). It will also be able to create copies of itself.

The token won't copy counters on Pack Rat, nor will it copy other effects that have changed Pack Rat's power, toughness, types, color, or so on. Normally, this means the token will simply be a Pack Rat. But if any copy effects have affected that Pack Rat, they're taken into account.

If Pack Rat leaves the battlefield before its activated ability resolves, the token will still enter the battlefield as a copy of Pack Rat, using Pack Rat's copiable values from when it was last on the battlefield.