She may have a sawdust filling, Anna--some originals do, and it does tend to settle, as will wool, cotton, and kapok over time. You can try to move the stuffing around, which can be hard on the original body textile, or you can just work around the issue--making a puffed sleeve can help "bulk out" the shoulder area, and you can set it onto a band that can slip over the chunkier bicep area.
Can you share an image of Mae's nekkid body? I can be more helpful with fitting suggestions for drawers that way. Though if you use millimeters to measure, you can actually scale down the free split drawers pattern and accomodate some of the more odd mid-century doll bodies (which can be VERY distorted, with extremely "German" thighs and hips.
Closures: small hooks with thread bars work well, as do hooks with thread eyelets (sewn holes in the weave of the fabric); buttons can be difficult, though they are used on some original doll clothing. Another period option with doll clothing is a hook/eye/eyelet as the functional closure, with a button or faux button placed on top decoratively.
To make the tiny holes a bit easier, outline the hole with a single thread, two or three times (tiny hand running stitch.) Work the buttonhole stitches with a single thread, and take your time. I've also successfully marked and worked a hole without opening it--using very tiny applique scissors to slice open the hole between the two purled edges when finished. It's fussy work, but *can* have a good result. Personally, I prefer to outline, open, and work, in that order, using a single strand of waxed thread. If you're working with fabric light enough to do for doll clothes, sometimes it's too light to take a buttonhole well; in that case, I lay a scrap of cotton organdy under the hole, work through it as though it were not there, and trim it away after stitching. It's a permanent, but very light, stabilizer.