Apart from immortality, in which the puppets can be destroyed and they does not recover. Does the puppets have the same amount of chakra or they only posses only their past live ability. Lets say if pain body were converted into a puppet. Would it have the Rinnegan? Or It would be a blind puppet? How does this puppet thing work. Does it require the person or thing to be alive before a puppet is made out of it or them? OR just ant body or shell is enough.
Edo Tensei and Puppets are very different.
For Edo Tensei:
Is a forbidden technique where, using a living person as a vessel, a deceased person's soul can be called back to the world of the living and bound to it. The vessel will then take on the form that person had in life, thereby reincarnating them to do their summoner's bidding.
A living sacrifice has to be made in order for the jutsu to work.
After the individual has been summoned and awakened, the summoner has no control over the reincarnated individuals with the exception of restraining their movements until they implant a special talisman, which is attached to the end of a kunai and implanted in the brain.
As for the Puppet jutsu:
They are most often humanoid-looking creations, but depending on the creator, can resemble anything. They are fashioned in a manner that uses every part as a weapon, giving the puppeteer a myriad of ways to manipulate it.
Sasori's Human Puppets:
A human puppet is a type of puppet created from human corpses, developed by Sasori during his time in Sunagakure. By removing the internal organs of a foe and preserving the body to prevent decomposition, as well as adding weapons and defences, Sasori can make powerful human puppets. These puppets are different from normal ones, as they retain their use of chakra and any kekkei genkai that the human host once had.
So, yes, the Pain puppet might retain its chakra. But it can use the Rinnegan only if the original Rinnegan eyes are present in the puppet's eye sockets. I'm not quite sure about the dead/living part, as we have no evidence about it.
A puppet is handmade and has no brain. It needs to be in close/mid range of the controller so that it can be controlled with chakra strings.
On the contrary, people reanimated by Edo Tensei are conscious, unless you bind their mind like what Kabuto did. They can also move freely and have their own will to do whatever they want.