@rachel I agree with the others; that's pretty impressive for a first dress.
Some fabrics do fray more than other! Handle with care and stay stitch where necessary is all I can suggest on that.
Re invisible zips - and ordinary zips. I put any zip in as soon as I can. If the back is just two pieces it's the first thing that gets done, but if there's a waist seam then obviously that has to be done before the zip. I do have an invisible zipper foot for the Husqvarna but I don't get on with it; I've worked out my own way of doing them with a regular zipper foot (the narrow one for
Singers.
1, Overlock or otherwise neaten the cut edge of the fabric on both sides.
2, Position one half of the zip where it needs to be (usually about 1/8" from fabric edge).
3, Stitch the zip tape into place but not very close to the teeth.
4, Position the other half of the zip where it needs to be.
5, Stitch the zip tape into place but not very close to the teeth.
6, Adjust the zipper foot (or move the needle) so that it is very close to the teeth and stitch a second time making sure that the zip is rolled outwards.
The first pass of stitching holds the zip in the correct alignment which means that all the attention can go to keeping the teeth rolled back and the stitching very close to them.
Sorting out the join between zip and seam can be a bit tricky. With a regular zip you close the seam below before inserting the zip but with an invisible you do it afterwards, and there is always a tail because it's impossible to sew all the way.