Do the stiches from skin grafting melt over time or are they permenantly in there?

Depends. If surgical staples or non-absorbable sutures - like silk or nylon - were used, then these have to be removed. ( if an absorbable suture - like catgut - was used, then no).
Removed in 1-2 weeks. Sutures are not left in permanently, the sutures are removed dpending on area and healing are removed in 1-2 weeks.