Removing old paint from wood ( professional vs DIY)
What professionals use depends on the situation. A chemical stripper, in my opinion, is not the best choice for the situation depicted in your photos. However, you do mention a door in your question, and sometimes a chemical stripper would be a convenient solution for intricate detail work provided the door could be removed and laid flat on a workbench or sawhorses. The cost for a professional to strip a door would depend on several factors. I always charge enough so that if I had to replace the door entirely I would not lose money, so it would depend on how fancy the door is.

I honestly think that you would save a tremendous amount of time, mess, and energy if you removed that wood frame from the wall and got new moldings with the detail of your choice. You could stain and varnish it before nailing it up.