Declension of article words and adjectives
As to the declension of adjectives and article words the German system is really complicated. German has three types of declension for adjectives. a) Der Mann ist alt. - The adjective in this position never has an ending and is invariable. b) der alte Mann - In this position the adj. can only have the endings -e/en (I call it simply the n-declensionsdeclension - German grammargrammars like the terms "weak" and "strong" and they use them everywhere, but I think they are more confusing than helpful.) c) ein alter Mann - In this position the adj. has the full endings (-er/e/es etc).
There are two sorts of "article words". Those that have the three gender endings -er/e/es such as dieser, jener, welcher etc And there is a second sort, article words such as ein, mein, dein etc which have dropped the endings -er/e/es. As ein/mein etc don't indicate the gender of the following noun any more, these gender endings are added to an adjective when you use an adj. between ein/mein etc and the noun.
So you say "der alte Mann ("der" indicates the gender, so the adj. does not need a gender-ending) and you say "ein alter Mann" ("ein" has no gender ending, so the adj gets a gender ending).
All this is complicated for beginners. And the logic of this system must be understood. And you need a good grammar for beginners with clear declension tables. The only useful grammar for beginners that I know was/is published by Diesterweg Verlag.