Is there any reason not to use an original idler arm in conjunction with a new pitman arm or should I buy a new idler arm as well?
IMHO no reason not to use it if you are just looking to drive the car. If you are racing there are advantages to some aftermarket parts.
Probably a dumb question but is the stud supposed to pivot?
It is not uncommon for them to be too stiff to rotate or pivot. Especially when new.
Should I inject some grease into it with a needle fitting on my grease gun?
Grease is always good.
And last, the idler arm fits snugly into the k-frame tabs as-is but I was reading about some new idler arms that come with foam-like washers. Do I need to add those? Not sure how I would get any in there though with the snug fit of the arm as-is.
The ones I have seen with foam were greasable and the foam was like dust seal to keep the grease clean.