Drywall – Is this kitchen wall parallel with the joists load-bearing

Chis is right in what he is saying. To further elaborate, I assume the structure has a full raftered roof. You need to be absolutely sure if any portion of the wall you want to remove is a supporting part. It is rare that a partition wall running parallel with the ceiling joists is a supporting wall, unless it spans across the center axis of the house perpendicular to the ridge board and some type of post or truss comes from a rafter to the top of that wall. When you look in the attic, are there any angle trusses attaching to the joists, most likely in the center of the building? Is there a center wall on the first floor that runs the length of the house? This is usually indicates a bearing wall. If your wall in question runs parallel with the rafters and joists it most likely is not supporting, especially if there is no joist above it. Since you will have to repair the ceiling after you remove the wall, you will need something to attach your sheet rock to, unless the existing ceiling runs the length and the upper plates of the wall you are removing are located below this ceiling. In any case, you will want to install a joist. If the removed wall is not supporting, it really doesn't matter if you install before or after. other considerations are if there is any electrical or plumbing in the wall. you gotta plan for that as well.

Substantial changes to a load-bearing wall really an engineer's review. The consequences of getting it wrong are unacceptable.

When it came time to take out a loadbearing wall in my place, I hired a contractor, who brought in an engineer to calculate exactly what size parallam beam would be needed to span the gap and how to provide the necessary support below the remaining stubs of wall which were now taking the additional load.