Hello,
1 There are no bad neighbourhoods that i know of in Florence. However if you prefer a VERY quiet place, i would look in the Oltrarno area, which is basicaly the area beyond the river. It is a bit out of the way tough.
2 I have no idea about Italian classes. If you have trouble finding any, get in touch, i have experience teaching English but i think i can adapt my skills to teach Italian.
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