You're asking a lot ... the panel suggests other problems that NEED to be addressed first; we can't be sure, because there is so much we can't see.
IF you have four wires -black, red, white, and bare- coming from the installed dryer receptacle, you're good to go.
IF the panel is designed to accept additional 'skinny' breakers, you're good to go.
Beyond that .... this is not a DIY forum, and we really think you ought to have a real sparky do the work. It's not just about 'making it work;' do that often enough, and there's a real mess to sort out.
