Learn Croatian: Kao prvo, to je propali posao. - First of all, that is a ruined business.

It comes from the verb propasti (to fail, to fall through). Grammatically, it is the active past participle (the form you normally use with biti to create the past tense). However, as you are learning in this lesson, it is used here attributively as an adjective. Instead of forming a verb tense, it acts just like a regular adjective describing posao, giving us "a failed business" or "a ruined business."

If the standard masculine past tense of propasti is propao, why does it end in -i (propali) in this sentence?

Because it has crossed over into being used as an adjective right next to a noun, it has to take adjective endings. The -o ending in propao is strictly the masculine singular marker for the verb form (e.g., posao je propao - the business failed). When acting as a masculine singular adjective in the nominative case, it takes the standard definite adjective ending -i, resulting in propali posao.

Is Kao prvo a set phrase, or could I just say Prvo?

You can absolutely use Prvo on its own, but Kao prvo is a very natural, fixed phrase meaning "First of all" or "In the first place." It is heavily used when a speaker is making a strong point or starting a list of arguments. In everyday speech, you will often hear it followed by kao drugo (secondly) and kao treće (thirdly).