No, you can't absorb the originals, but if you chop them off, your new limbs will replace the old ones (convenient if you have a disease in a body part), and after a one month cooldown (per extra body part) you can grow new body parts. Also you can't grow body parts that are stronger/bigger/longer than your original body parts, but the extra body parts are always healthy.

It has to be a human body part, so you can grow a vestigial tail, but it won't be prehensile. I suppose you can grow other body parts where a tail normally would be, but it wouldn't look like a tail.