Learn Italian: Non mi piacciono le frange corte.

The singular is frangia (fringe or bangs). The rule for feminine nouns ending in unstressed -cia or -gia is to look at the letter right before it. If it is a consonant (like the 'n' in frangia), the 'i' is dropped in the plural, making it frange.

Does dropping the 'i' in frange change the pronunciation of the 'g'?

No, the 'g' remains a soft sound, like the 'j' in "judge". In Italian, the letter 'e' already makes the 'g' soft, so keeping the 'i' is not necessary for pronunciation.

Why is the verb piacciono plural here when the English translation says "I do not like"?

In Italian, the verb piacere works backwards compared to English. The sentence literally means "Short fringes are not pleasing to me." Because the grammatical subject is the plural noun le frange, the verb must be the plural form piacciono.

Does frangia refer to the fringe on clothing, or hair?

It can be both! While it means "fringe" on clothing or a rug, in the context of personal style, la frangia is the standard Italian term for hair "bangs". So frange corte here means "short bangs".