Hi Lloyd, sorry to hear about your leaky problems. Ya, the octave key will make you jump octaves if there is even the slightest leak there but it's only a small pad that needs to be changed.
A true, complete overhaul on a sax can cost more than some saxophones are worth, so for a cheap student model you shouldn't really worry about investing in a complete overhaul. The tiny and specific detailed work that a repair pro gets into is not noticeable enough for a beginner on a cheap horn.
Usually, just replacing the bad pads will get the thing working better than good enough in my experience.
ps
if anyone is shopping for a sax on eBay beware, there are some really crappy cheap ones made in China… some repair guys won't even work on them for fear of them falling apart!