Is is possible to change the eye shape in this manner? (Photo)

It sounds like you are looking for a more almond shaped eye. A skilled oculofacial plastic surgeon would be able to do a closed full canthal release/resuspension with small adjunctive midface lift to elevate and elongate the lateral canthal angle. In hands of a skilled surgeon, this is relatively low risk however you need to be prepared to be overcorrected at first having a "cat eye" and know the reality that mother nature is pretty powerful and if you want to maintain a natural, non surgical look, there is a chance that after a year or two the results will not be significantly different than pre op.

loose skin can be treated with proper superficial liposuction (VASER + Jplasma/Renuvion or InMode BodyTite) and/or threadding such a s PDO Novathreads or Instalift. Ultherapy and/or kybella can also be tried as non invasive options to tighten and sculpt the neck and contour the eye