Hey Arnab, As its an off season i dont think you would need to book a stay for yourself in any of the places in spiti valley ... You can get them easily ... And for your question on access to mud Village after reckong peo ... you can get that conformation in tabo Village which comes before you reach Kaza ... Hope this helps you ... Happy Travelling Bro!!!
Hi, the only open route available to reach Kaza would be from Kinnaur side, so you have to board the Reckong peo - Kaza bus. There would not be any public transport for Mudh, you will have to either walk or get a private taxi. I have attached with this comment few options for you to stay in Kaza and Reckong Peo