Does Russian have "common" endings?
To make this easier to understand, I'll use an example from German. Personal pronouns have different endings based on gender and case. However, the endings are based off those of the articles for "a", making them easy to learn. mein=ein, seine=eine, unseren=einen. Adjectives also follow a similar pattern. Does Russian just so happen to have a few connections like this, or are all the sets entirely different? Just wondering.
Yes, but they differ depending on whether the last letter of the stem is hard or soft. The common adjectival endings are (for male, neuter, feminine, and plural): -ый/ий, -ое/ее, -ая/яя, and -ые/ие. The first ending is for hard endings and the second is for soft endings. It can be difficult to tell whether a word is hard or soft, the best way is to memorize the spelling rules (there are 3 - the 5-letter, the 7-letter, and the 8-letter). These endings, however, are only for the nominative (regular) case, so if a word is a direct or indirect object or after a preposition, etc., it's ending is different.
Yes, here they are:
8-letter - Never write 'Я' and 'Ю' after Г, К, Х, Ш, Щ, Ч, Ц; write 'А' and 'У' instead, respectively. 7-letter - Never write 'Ы' after Г, К, Х, Ш, Щ, Ж, Ч; write 'И' instead. 5-letter - Never write an unstressed 'О' after Ш, Щ, Ж, Ч, Ц; write 'Е' instead.
Adjectives, adjective-like pronouns and third person pronouns share all the endings in all cases except nominative and accusative.
Also, all the ending have two versions, palatalised and non-palatalised, so what may look different is actually the same ending.
Example for masculine:
nominative: большой, синий, этот, он, один ← quite irregular here
genitive: большого, синего, этого, (н)его, одного
dative: большому, синему, этому, (н)ему, одному