Drywall – Is it normal to have a bulge along the seam between pieces of drywall

Personally, I would just build a rectangle out of 2x4s slightly smaller than the hole, lower it into the hole flush with the existing framing, then screw it to the existing framing. That will give you a nice surface to attach your new drywall to. Depending on the size of the hole, you might want a cross member in the box as well so your drywall isn't spanning too big of a hole unsupported.

As for cutting back the existing drywall - I wouldn't bother with that for a couple reasons:

First, you're likely to run into issues with the nails or screws that were used to originally attach the drywall to that framing. If you cut around those, then the old drywall isn't going to have a very secure connection to the framing unless it was glued. And if it was glued, then you have the problem of the glue residue getting in the way of the new piece you want to put on.

Second, the damaged areas of the drywall are well within the areas that you'll need to mud over anyways - figure on mudding out at least 6-12 inches on either side of the joint. So you're really not saving yourself any work by cleaning that up.

When measuring, I tend to assume the seam between drywall and the adjacent surface (wall or other piece of drywall) will eat at least 1/8" from my measurements, and sometimes 1/4". You're not intentionally leaving a gap, so adjacent pieces are pushed as tight as you can against each other (unless you have a gap to other pieces of drywall on both sides, in which case you center it). But with rough edges, you have to account for this extra space to avoid forcing the drywall into place. This impacts you differently depending on where you're measuring:

• When measuring for cutouts, that extra offset can sometimes be added (near side), and sometimes cancel out the original offset (far side), so be careful to double check your measurements (or use a rotary cutout tool so you don't have to measure those with any accuracy). Remember to transpose your measurements, especially for ceiling cutouts, since the drywall will be flipped from resting on the ground to being suspended over your head, where left becomes right. I often mark two sides that all my measurements will be based off of first so they don't get mixed up.

• When fitting drywall into an opening (the last piece that has to go in) you have to deduct for both sides. I'll start with a 3/8" deduction and be ready to rasp down any high spots. Always measure both sides of the opening (4 measurements, not just 2) since things often aren't square.

• On the ceiling, you've got the drywall on the wall to hold up the ceiling and cover the gap. You just want the gap to be under 1/2". I would subtract 1/4" from a measurement to a wall in this situation.

• When measuring for walls, it's mainly for the vertical joints to the next wall, and those gaps are often covered by door trim or the drywall on the next wall in a corner. Drywall is installed to the top of the wall first, supporting the ceiling that was already installed, and then it's installed on the bottom half of the wall. The gap around the floor can be at least 1/2" and is often closer to 1" and will be covered by trim.

• When measuring for outside corners, don't leave any allowance. Instead, use a rasp to knock down the edge until it's perfectly even with the adjacent wall.