You got the rules for forming the verb participle correct. The verb participle can be used in several ways, among them as an adjective, in which case it agrees in gender and number with the noun it modifies. But the meaning is still that of a participle. For example, the participle of manchar ("to stain") is manchado ("stained"), so "Esta camisa está manchada" means "This shirt is stained".
The participle of cuidar is cuidado, which means "cared for", and is generally used with an adverb, e.g. "El jardín parece bien cuidado" ("The garden looks well cared for").
Cuidadoso is not a participle-derived adjective; it's a derivation of the noun cuidado, which means "care" (as in "take care" or "treating something with a lot of care"). The derivation is done by adding -oso (which turns into -osa, -osos, -osas as needed, of course). There are many words with this suffix, but they're not derived from verbs and you cannot derive them from any word you choose; you have to check if they exist in the dictionary, and see what the meaning is. Cuidadoso means "careful", not "cared for". Other similar words you might find useful are ansioso ("anxious"), asombroso ("astounding"), caluroso ("hot"), etc.