The reason for not using a blender is that the the blender may liquefy it. When you make a blessing on a class of food it is assumed that all of that type of food is included. So if you made a blessing on vegetables for the appetizer and then had potatoes in the main course, if you said another blessing it would be in vain.
The prohibition to eat before feeding one’s animal is only eating a full meal, so you could make a blessing and taste a bit of food prior to feeding the animal.