Nodes could avoid the hard work that represents finding the "nonce" to get a hash with a lot of zeroes in a row. Then anybody could afford a node and Bitcoin would be a lot more decentralized.
Nodes aren't the same as miners. Miners have specialized equipment which does the computations to find the hash that is less than the target. Nodes are just computers that keep a local copy of the blockchain and fully validate all transactions and all blocks it receives. Nodes would still be the same affordability since the blockchain would be the same size and validation still is the same.
Bitcoin client can establish that nodes must always try to reach the block size limit (today 1 mega), and transactions must be ordered in alphabetical and time stamp order into the block, then all nodes could achieve almost exactly the same block, then find the block hash and try to find concensus (on this hash) among all the nodes of the bitcoin network.
How would you achieve consensus? My node might choose to not relay or store certain transactions in the mempool while yours does. By including different transactions, different hashes will be produced. Consensus cannot be achieved this way. Even if the mempool rules were fixed, due to the propagation of transactions, some nodes might have transactions that another doesn't. This also has an issue of a spam attack preventing use of Bitcoin transactions. Say an attacker with a little bit of computational power creates thousands of transactions beginning with the letter "a" and spams the network. Then all of your blocks are filled with spam and legitimate transactions are not included.
From this concensuated hash then we pull only the númbers and obtain a BIG NUMBER.
What do you mean "pull only the numbers and obtain a big number"? The hash itself is a big number, 256 bits, represented in hexadecimal format.
Also we make a circular list of active nodes (nodes that have validated transactions in this last block) and we order them alphabeticaly in a circular way (the last node is next to the fist node of the list).
Starting from the first node of the list, we use the BIG NUMBER to count around the circular list until we pick the consensuated winner.
This winner node takes the new created bitcoins and the transaction fees...
What prevents someone from forking the blockchain and doing double spends? There is nothing that prevents a malicious user from creating thousands of blocks and attempting to fork the blockchain. PoW and PoS prevent this because it cost resources in order to fork the blockchain and attack the network. Your proposal has no inherent protection so it would be vulnerable to various double spend attacks and blockchain forks.