If I respond to a permanent resolving is it in play when my spell/ability resolves?
Yes, though it happens in a complicated way.

Golgari Charm's first mode creates a continuous effect that modifies characteristics (power and toughness). It only affects the creatures on the 'field when it resolves.


  611.2c If a continuous effect generated by the resolution of a spell or ability modifies the characteristics or changes the controller of any objects, the set of objects it affects is determined when that continuous effect begins. After that point, the set won’t change. (Note that this works differently than a continuous effect from a static ability.) [...]


(Same goes with Bile Blight. Any Pack Rats entering the field after it resolves won't be affected by it.)

That means the following will happen:


You cast BB
In response, opponent activates his PR's ability
In response, you cast GC
GC resolves: 3x 2/2 PR
PR's ability resolves: 3x 3/3 PR + 1x 4/4 PR
BB resolves: 3x 0/0 PR + 1x 1/1 PR
SBA kills the PR with non-positive toughness: 1x -2/-2 PR
SBA kills the PR with non-positive toughness: No PR


It's a little cleaner if you wait before casting GC. 


You cast BB
In response, opponent activates his PR's ability
PR's ability resolves: 4x 4/4 PR
You cast GC
GC resolves: 4x 3/3 PR
BB resolves: 4x 0/0 PR
SBA kills the PR with non-positive toughness: No PR


No matter the order, creating a 5th PR before BB resolves would save them all. But which of the approach you used will affect how strong they are.


Using the first approach, he'll end up with 3x 1/1, 2x 2/2.
Using the second approach, he'll end up with 4x 1/1 and 1x 2/2.