1. You should not drive with any broken control arms. Broken bushings are one thing, but don't drive if the bolts are loose or broken, or if the arm itself is in two pieces.
2. You do not need to measure anything with stock control arms. Adjustables are another story.
3. You can replace one at a time, keeping the bolts on decently tight, then drop jeep on all 4 tires, loosen the bolts again and torque to spec.
4. If you cut the arms out its fine, just make sure you save a few "example bolts", bolts that did not get cut up too bad so you have a frame of reference. Just want to double check that your new hardware is the correct size, grade 10.9, flange or no flange, etc. etc.
5. I found that removing the gas tank made a huge difference when doing the rear suspension. It's just too much in the way of everything. You can even install the whole rear suspension then add gas tank at the end- it only makes a difference of about a quarter inch in ride height (won't affect track bar or sway bar link adjustments significantly).
When you get the rear shocks out, throw away the original upper shock bolts, they are 8.8 or something. Get zinc coated 10.9 replacements and use anti seize generously. then tighten back up with only 1/4 inch drive. You will never have problems again.
You're supposed to torque the control arms with the weight on the axle/at ride height so either all 4 tires on the ground or jack on the axle, no stands on frame. The rear lower control arms by the axle side will be difficult/impossible to get a torque wrench on, on the ground, depending on what wheels and tires you have. For those two bolts, I tightened on the ground as much as possible, then I raised up the rear axle on a jack and removed one tire at a time to get them torqued.