Learn Farsi: اولین سالگرد کی است؟

This uses the Type 2 ordinal number format. For most numbers, you add -omin (like dovvomin for "second"), but "first" is a special case built from the base word avval. To make it a Type 2 ordinal, we just add -in to get avvalin.

Why isn't there an Ezafe (the "e" linking sound) between avvalin and sālgard?

Type 2 ordinal numbers (ending in -in or -omin) always come before the noun they describe. Because they are placed in front of the noun instead of after it, you do not use an Ezafe to connect them. It is simply avvalin sālgard.

How is the word sālgard (anniversary) built?

It is a compound word. It combines sāl (year) with gard (from a verb root meaning "to turn" or "to return"). So it literally translates to the "turning of the year."

How would a native speaker say key ast in everyday conversation?

In spoken Farsi, the verb ast (is) is almost always shortened to an -e sound attached to the previous word. A native speaker would simply say key-e instead of the formal, written key ast.