Congratulations on the adoption of Barney and Cassie! The behavior you're describing is nothing to worry about. In fact, many cats exhibit that style of eating.
Sometimes a cat will use its paw to spoon out the food onto the floor if the food bowl is not the right size for the cat. Make sure the bowl isn't too deep, large or small. You may want to try using a shallow bowl, which applies to the water bowl as well. Also, don't use a double bowl because some cats don't like having their food and water so close together.
If the bowl is the correct size, then your kitty may just not like putting its face into the bowl. With some cats, though, the behavior is simply play-related. Sometimes they grow out of it, and sometimes it becomes a habit.
Occasionally some cats -- particularly kittens -- will also poke at their food with their paws. This likely originates when they first learn to eat from a bowl. If a cat isn't sure about something, it may "test" the food first in this way with a paw.
To control the mess, you can buy a pet place mat that has a raised edge all around. This will also help contain any liquid spills.
