Moving back slider door
CrpntrFrk is right. There's a high likelihood that the wall is a bearing wall since it is an exterior wall. It is very, very rare that an exterior wall is not a bearing wall. Moving that door is certainly possible, but it is a pretty involved job, and is probably not a good idea unless you have some experience with framing or know someone knowledgeable that will help you out.
Removing the slider and installing French doors is much more DIYer friendly for sure. Still an involved job, but you don't have to reconfigure the header, etc.