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  Yes, they can be neutered.  I don't know about the age to compete - we do it for fun and don't compete.
 I would start with a puppy class and general training at this age.  In order to properly do agility you have to have control of your dog - such as stay so that they wait to begin.  You also have to have a good recall - even then a young dog will get the zoomies all over the place when you're trying to get them to follow a course.
 
 One very important thing is no jumping till they are done growing - usually around a year old.  Even though they jump on their own when playing, it's very different to jump on command.  I would consult with your vet for guidance on when it would be proper to train for agility.  With mine, we did general obediece till they were over a year old and then started with agility.
 
				__________________ Karen and the Kids  Sadie and Beemer  |