be moving: is it a present progressive? showing vs shown

[anhnha]

Public opinion appears to be moving in their favor, with a recent poll showing about 50 percent of French support same-sex marriage, down from 65 percent in August.
More:Hundreds of Thousands in Paris Protest Gay Marriage - World - CBN News - Christian News 24-7 - CBN.com

What is grammar term used for "be moving"? Can I call it present progressive?
Can I replace showing by shown?

 

[Rover_KE]

What is grammar term used for "be moving"? Can I call it present progressive? Yes.
Can I replace showing by shown? No.

Rover

 

[5jj]

What is grammar term used for "be moving"? Can I call it present progressive?

I'd call it a 'progressive infinitive'.