German like English, distinguishes between possessive determiners / possessive adjectives on the one hand and possessive pronouns on the other hand.

For example, in English, we have "your dog" (possessive determiner "your") but "yours" (possessive pronoun).

Possessive determiners stand before a noun, but possessive pronouns (like other pronouns) stand by themselves, in place of a noun.

In German, possessive determiners and possessive pronouns mostly have the same endings, but in the nominative singular, the possessive determiners have no endings for masculine or neuter nouns while the possessive pronouns do.

Thus Dies ist mein Hund und das ist deiner (masculine) and Dies ist mein Pferd und das ist deins (neuter). Compare English "This is my dog and that is yours". (I wonder whether the -s on "yours" is related to the -s on deins.)

Because this is the comparative form of groß and not just a declined form of the positive: https://www.cactus2000.de/deutsch/adject/showadj_en.php?adj=gross&mode=1

Why is it "Mein Hund" and not "Meiner Hund"?

Just the way it is.

The indefinite articles ein, kein and the possessive determiners mein, dein, sein, ihr, unser, euer, ihr have no ending for masculine nominative, neuter nominative, or neuter accusative.