Learn Farsi: درس دوم سخت است. - The second lesson is hard.

It is spoken but not written. You pronounce it dars-e dovvom. Ordinal numbers that end in -om (Type 1) act like regular adjectives. They come after the noun they describe, so you must use the Ezafe to link the noun to the number.

The word for two is do. Why is second dovvom instead of doom?

When the base number ends in a vowel, Farsi often adds a 'v' sound before the -om suffix to make it flow better. So do becomes dovvom. You will see this same pattern with se (three), which becomes sevvom.

Could I say dovvom dars instead?

Not with this specific word. Type 1 ordinal numbers ending in -om must always follow the noun. However, Farsi has a second type of ordinal numbers that end in -omin. Those are placed exactly where you suggested: before the noun, without an Ezafe (dovvomin dars). Both mean the exact same thing.

How does ast change in spoken Farsi for this sentence?

In casual speech, ast (meaning 'is') shrinks down to just an -e sound attached to the word before it. A native speaker would say dars-e dovvom sakht-e instead of sakht ast.