You can touch them if you need too, but I wouldn't make a habit of it. Be sure your hands are clean/wet. I suppose you could pet it, but I suspect most healthy axies wouldn't really like it and they'd either swim off at the first touch or try to bite the finger as it approaches. As for picking it up, if you mean out of the water. This would be not advisable unless you're transferring to another aquatic place. The main problem is that handling them frequently will damage their slime coat. The slime coat is a protective layer and damaging it is a stress and may open them up to infection.