Learn Portuguese (Portugal): O modelo velho tem um som pior.

No, you generally shouldn't. Just like in English we say "worse" instead of "more bad", Portuguese uses the irregular comparative pior instead of mais mau.

Som is a masculine word. If we were talking about a feminine word, like imagem (image), would the word pior change to match it?

No, pior is exactly the same for both masculine and feminine words. You would say um som pior (a worse sound) and uma imagem pior (a worse image). However, it does change for plurals: if it were "worse sounds", you would add "-es" to make it sons piores.

Why do the adjectives velho and pior come after their nouns?

In Portuguese, adjectives usually come right after the noun they describe. This is why velho comes after modelo and pior comes after som. While some adjectives can occasionally go before the noun for artistic emphasis, placing them after the noun is the standard rule you should follow.

Is velho the best word to use for an "old" model of an electronic device?