The Blue-diademed Motmot is distributed from southern Mexico through Central America to Panama. See the distribution map at Birdlife International.

It is now recognised as a species by several authorities such as the HBW and Birdlife International Checklist, Howard & Moore and the South American Classification Committee (See their decision here) but is still lumped as Blue-crowned Motmot by Clements and others.

The bird in photo 1 was perched within a metre of the ground and has an uncharacteristic colour and texture to its belly. I have seen this on smaller birds such as Social Flycatcher Myiozetetes similis and it turned out to be a brood patch so I wonder if this is the explanation here.