The first そう comes after 終止形 of verbs and adjectives. All 終止形 forms, negatives, passives, causatives, present and past etc are possible.
This means "I hear(d)/read that... " (not looks/seems like as assumed in the question).
彼は死んだそうだ I heard he died
あのケーキは美味しいそうだ I hear that cake is declicious
彼は嫌われていなかったそうだ They say he wasn't hated.
This そう is often listed as a particle, but it really behaves like a noun, and is almost always followed by copula. It has no 連体形, i.e. 静かだそうな is ungrammatical (unless な is the sentence-ending particle). Also, the following copula is not used in the past tense, i.e. 静かだ(った)そうだった does not exist, but 静かだったそうだ does.
The second そう comes after the 連用形 of verbs and the stem of adjectives. 良い(いい) and 無い have irregular forms 良さそう and 無さそう. Negative verb forms ~ない become ~なそう, but ~なさそう is often heard, although it's considered incorrect.
濃{こ}そう, 静かそう, 行きたそう, 食べなそう looks dense, seems quiet, looks like sby wants to go, looks like sby won't eat
The result of this is a na-adjective meaning "looks ..." or "seems ...". For action and state-change verbs, it can also meen "about to ..." or "looks like sby will ...".
Being a na-adjective, this form can be used both in the 終止形 and 連体形 forms (and negative forms etc.),
美味しそうなケーキ a delicious-looking cake
このケーキは美味しそうだ this cake looks declicious
死にそうな人 a person (looking like he's) about to die
彼は死にそうだ (he looks like) he's about to die