Time allowed to a node to react to verify a transaction and number of verifications? Do the person acting as full nodes have to be active and online around for a particular decided time, like a job where you have to be around your machine because a transaction for verification can pop up anytime and if you are not around what happens then?
Also, the Bitcoin has more than 30000 nodes, how many verifications it actually need to become a part of ledger because how can you guarantee that this number of people will verify it in this fixed amount of time otherwise the wait could go indefinite?
You seem to misunderstand how transaction validation and finality works.
Nodes validate transactions as they receive them in the mempool or in new blocks - these validations check for standardness (for mempool txs), and consensus compliance  (ensuring there are no double spends, valid utxos, etc).
However, a transaction is not final simply because a number of nodes have confirmed it. A transaction is final ONLY if a miner includes it in a block AND that block is accepted as valid by the network. This finality happens regardless of whether there is 1 node on the network, or 30000.
Note that even after being mined into a block, conventional wisdom says to wait for new blocks to be mined on top of that block, to provide a reasonable guarantee against minor forks rolling back a transaction you consider final. Most exchanges and service providers wait for 2-6 confirmations before considering a transaction truly final.