It shifts fine. Not like my modern road bikes indexed brifters... but OK. Actually I think the stem mounted shift levers are easier to use than the down tube mounted levers. Of course I am an older dude.... and felt very lucky to have bicycle with gears back in 1964. So the friction shifters aren't a problem for me. An afternoon of shifting and listening to the sounds of the chain... and you'll have it mastered too.

Hard to guess rust damage... particularly from a picture. But a little really soapy slick water and some crumpled up aluminum foil knocks off surface rust without damaging metal or (if your careful) even paint.