I thought that "Táim go dona" means something like "I'm not doing well", "I'm in a bad condition", and "Táim dona" means "I'm bad", as in "I'm a bad person". Is that wrong?
Yes. dona requires a predicative use (go) when used with tá and means "bad" as in unwell. For the second sentence, you'd more likely use dána which means bold.
It might be worth adding here that when you say 'bold' here you're using it in its Hiberno-English meaning of 'naughty' :).
how is this different to "droch" meaning bad?
Droch- is a prefix or the first part of a compound word, not an independent word.
and where does "olc" stand in all this"
Why not "is go dona mé"?
That's not a valid sentence because you used the copula "is", which is only used to identify and equate two nouns.