Learn Hardcore German: Die Farbe an der Wand ist grün.

In German, all nouns are capitalized. Farbe is a noun, so it gets a capital letter.
Adjectives like grün are only lowercase (unless they start a sentence or are part of a title).

Why do we use the article die with Farbe?

Farbe is a feminine noun in German.
In the nominative singular (the subject of the sentence), feminine nouns take die as their definite article.

Why is it an der Wand instead of auf der Wand or an die Wand?

an with the dative case expresses a static location on or at a vertical surface.
Wand is feminine; dative singular of die is der, so an der Wand = “on/at the wall.”
auf der Wand could imply something lies flat on the wall’s surface (e.g. a poster).
an die Wand (accusative) would indicate movement toward the wall (“to the wall”).

Why isn’t grün inflected as grüne or grünen here?

How would the sentence look if grün were used attributively before Farbe?

It would be:
Die grüne Farbe an der Wand.
Here, grüne is attributive and takes the weak ending -e for feminine nominative singular.

Why is the verb ist in the second position of the sentence?

German main clauses follow the Verb-Second (V2) rule: the finite verb appears in the second slot, regardless of what element comes first.

Could I simply say Die Wand ist grün instead?

Yes.

Die Wand ist grün means “The wall is green.”
Die Farbe an der Wand ist grün emphasizes the color itself rather than the wall.

What’s the difference between Wand and Mauer?

Wand refers to any wall, especially interior walls or vertical surfaces.
Mauer usually denotes an outdoor or freestanding wall, often built of stone or brick.