ok ... let's see what i can tell you.
1) minarelli calls for sae-20 non-detergent oil. some people have claimed that even detergent oil is good and that other ranges of oil are fine. i'm something of a purist, so i use straight non-detergent sae-20. it's cheap, so why not.
2) the cimatti w/ the rear tank is the "city bike" the other is probably the "twin sport" (there is one of these in kzoo and a few city bikes). i've no idea about the one you describe. see if you can find a marking or post a picture. sounds like a find.
3) not sure about using a battery for lights, but other people have rigged up stereos and other things. search for those key words, or maybe some of those people will repost.
4) use a ulock to keep your moped. use kryptonite ulocks. the standard moped key lock under the handblebars is very very easy to break. and cutting through chains isn't that much harder. ulocks are sturdier. mopeds get stolen. think about it, they're easy to pedal start. someone's on it ... and they're off. bye bye precious moped.
5) the wheels you mention are mag wheels. you can get some easily enough. later mopeds have them, so you can probably get some to fit. i personally like the classic look of the spoke wheels ... but that's my preference.
post some before/after pics. good luck!