Is there a metro mover that goes from the airport to downtown Miami?

No

The Metrorail( train) takes you to downtown.

The Metromover will not take you to the airport, but the Metrorail will. You need to use the Orange Line to get there.

Yes, first you take the MIA mover to go to the train station. At the Metro rail you take the Orange line that goes to Dadeland North, South Miami, University, Douglas Road, Coconut Grove, Vizcaya, Brickell, Government Center, Historic Overtown/Lyric Theatre, Culmer, Civic Center, Santa Clara, Allapattah or Earlington Heights stations.

You can take the bus to Miami city center or malls for 2.75$ .

Yes

I think downtown does not go any, I use uber, I think it's the best option, it does not reach $ 20