which are considered bestimmt or unbestimmt articles?
we have many articles that can supersede any name in German. Depending on whether this article is definit/bestimmt or undefinit/unbestimmt the ending of the preceding adjective changes. Which of the following fall into either category:
diese/er/es/en/em, jede/er/es/en/em, manche/er/es/en/em, solche/er/es/en/em, welche/er/es/en/em and all possessive articles like (mein, dein, sein, ihr... etc.)?

Question

which are considered bestimmt or unbestimmt articles?
we have many articles that can supersede any name in German. Depending on whether this article is definit/bestimmt or undefinit/unbestimmt the ending of the preceding adjective changes. Which of the following fall into either category: 
diese/er/es/en/em, jede/er/es/en/em, manche/er/es/en/em, solche/er/es/en/em, welche/er/es/en/em and all possessive articles like (mein, dein, sein, ihr... etc.)?

Answer

Your terminology seems a bit unusual to me: Normally only "ein" and "der" (and their inflected forms, of course) are called articles in German, while all the words you mention are classified as pronouns. Anyway, it's

– dieser/jener/mancher/welcher schwarze Hut
– mein schwarzer Hut

»Solch-« is a bit special, see e.g. http://www.canoo.net/services/OnlineGrammar/Wort/Adjektiv/Deklinationstyp/Schwankend.html#Anchor-solcher-48213