What is the Design of Bitcoin storage? How is bitcoin network stored and shared across the network? For instance, where is the data of UTXOs for each wallet is maintained?
What is the Design of Bitcoin storage?
  where is the data of UTXOs for each wallet is maintained?
  


There's no need for every wallet to use the same storage format. The precise details of the storage format may be proprietary secrets or may be undocumented other than in the source code for that specific wallet.

This question could only be answered with some certainty for a specific version of a specific wallet.


  
  How is [the blockchain] stored ... across the network?
  


Every full node keeps a complete separate copy.

Lightweight nodes (SPV etc nodes) each maintain a pruned copy of the blockchain that only contains blocks with unspent transaction outputs.


  
  How is [the blockchain] ... shared across the network?
  


That is a rather separate question, there's probably an answer already here for that. Its probably described in Nakamoto's original whitepaper which is easy to find.

See also


How are transactions broadcast to the rest of the network?
https://en.bitcoin.it/wiki/Network
https://en.bitcoin.it/wiki/Protocol_documentation

which contains information of this sort: