Does the quality of JPEG pictures changed when cropped in any app editing pics?
If you crop an image you simply lose that info outside of the boundary of the crop. Normally "Quality" is lost during the saving process, depending on the algorithm used and the settings defined by the user.
But this is to board, because some application could resize the photo when opened, uploaded, etc.
what can I do to have a high-resolution JPEG pics and unchangeable (vector) format?
You can have any photo inside a vector program, Illustrator or Corel Draw, and you can have it in two different ways.
Embedded: where the photo is inside the file. It will not lose any data.
Linked: The photo is linked to externally. Any change you made to the original file will be updated inside the vector file. If you delete or change the name, the link will be broken.
You can put a photo inside a path, typography, shapes, add gradients, transparency, blending modes, etc, so yes, you can simply put an image inside a vector based program.
So simply put a photo inside, place it, import it, copy-paste it. Depends on your needs.