Is air entrained concrete stronger?
Can mortar be air entrained as well?
Can air entrained concrete be used for footings or foundation?

Yes, yes and yes. http://www.lime.org/BLG/McGinley.pdf

Air entrained concrete is more durable (especially with regard to freeze-thaw cycles) and more workable.
Too much air-entrainment can greatly reduce compressive strength as the microscopic air bubbles are replacing sand, cement and stone. Air content can be measured on site. This site offers some discusion also:Air-Entraining

Thank you all! Very helpful!