1) The first answer that comes in my mind is that «sciocca» is a woman while «scemo» is a man :-) joking apart, «sciocco» is lighter than «scemo», you say «non fare lo sciocco» to someone is joking you, «non fare lo scemo» to someone is annoying you. Also, you can use «sciocco» for events: «una sciocca superstizione», «uno sciocco incidente», «una sciocca coincidenza»... as a synonimous of insignificant, banal... «Sciocco» can also be a dish poor in salt.
2) Just because elision is mandatory on singular but not on plural, where is almost never practised. Anyhow it isn't forbidden, you can write «l'edicole» if you want, but it will sound out of date or aulic; be aware that you can write «gl'italiani», «gl'inglesi», but you can never write «gl'americani», «gl'europei» because the sound would change from «gli...» /ʎi.../ to «gla...» /gla.../ or «gle...» /gle.../ and this is not allowed by the rules of elision.
3) If you mean «palestra» as a «kind of place», it goes without articles; if you mean it as a «real place» that is not unique and you haven't yet introduced to your interlocutor, it goes with the indefinite article; if you mean it as a «real place» that is unique or you have already introduced to your interlocutor, it goes with the definite article.
4) One can only go back to his/her gender according to articles or adjectives, but not to his/her relationship unless your interlocutor already knows it or you specify it, for example: «mia nipote, la figlia di mio fratello, ...» or «mio nipote, il figlio di mia figlia, ...»; of course, if you say such a sentence: «mia nipote mi ha chiesto: "zia, posso studiare italiano con te?"» all makes sense by itself. The same problem you can find with «ospite» that can mean both «host» and «guest», only the contest can help you.