In case 1, where the use who posts the image owns the rights to it, s/he has the right to share it with anyone that s/he wishes, and the right to create or publish a modified version, and the right to provide the image to any application that s/he wishes, including a third party application. Nothing in the Instagram Teems of Use purports to restrict these rights.
In case 2, where the poster does not own the rights to the image, s/he cannot legally post it to Instagram at all without permission from the holder of the copyright. This may be in the form of a more-or-less open license, such as a CC license, or in the form of a direct grant of permission from the rights-holder to the poster. But in the absence of one of these, the mere act of posting the image to Instagram is an act of copyright infringement (unless the image is out of copyright, due to age or some other reason). The poster could be sued by the rights-holder for such infringement, and made to pay damages.
Further in case 2, the poster would need permission to create, or to have someone else (including an app) create, a modified version of the image. This would be a derivative work, and the creation of derivative works is one of the exclusive rights that the copyright holder has. So again, the creation of such a modified version would be an act of infringement, in the absence of proper permission from the rights-holder. And furthermore, distributing such a modified version would be a further act of infringement, unless the poster had permission to do this.
If the image had been published with a sufficiently permissive license, such as a CC-BY license, (without an ND or NC restriction) then the poster would not be infringing and would need no additional permission from Instagram. The same applies if the poster has a direct grant of permission from the rights-holder that includes making and distributing derivative works. In the absence of permission from the rights-holder, the poster is infringing, and Instagram cannot grant such permission if the rights-holder did not.
This all should be true in any country that subscribes to the Bern Copyright Convention, which is now almost every country on earth. Exactly how a rights-owner might go about taking action against an infringer would vary by country, as would just when an image goes out of copyright, but the general scheme should be the same.
This is all general information, and should not be considered to be specific legal advice. I am not a lawyer.