the first node validates your transaction, and if it is true, it redistributes it to other bitcoin nodes until it reaches the last node
Every node verifies every transaction it receives, not just the first node.
Blocks (blocks of transactions) are arranged in a series of numbers, new transactions get added to new block whenever new transactions are created.
That's not accurate. Whenever a new transaction is created, it is added to the pool of unconfirmed transactions known as the mempool. Miners then pick a subset of transactions out of the mempool (usually the ones paying the highest feerates) to include in the block they are attempting to mine.
Miners compete to find the nonce of that transaction, whoever has the most hash rate will likely solve the puzzle and include it in a fresh block.
Again, not correct. Miners compete to find the nonce (or other variable data) required for the hash of the block in question to be below the current target. Transactions do not have a nonce.