In short: No.
As the blockchain for something like BTC grows, does that affect the time needed to verify new transactions
Since the blockchain is immutable - or at least all but the last few blocks. It doesn't need to be verified more than once. Nodes will create, from a single pass of the blockchain, a list of spendable coins - the unspent transaction outputs (UTXOs) and use that UTXO list to verify future transactions. The UTXO list is a lot smaller than the blockchain and doesn't grow as fast. Spent UTXOs are removed from the UTXO list.
Changes in the size of the UTXO list are presumably driven by factors such as:
- Growth in monetary amount of issued Bitcoin. The total amount of BTC grows towards 21 million, but at an ever decreasing rate due to the halving process applied to block rewards. In other words, Coinbase transactions necessarily create new UTXOs.
- Fragmentation of UTXOs in the UTXO set is probably driven by, among other things, the long term trend of an increase in the value of Bitcoin. If a Pizza used to cost 1000 BTC and today costs 0.0001 BTC, one might expect that there would as a result be a lot of small UTXOs rather than a few large UTXOs.
- Agglomeration (or consolidation) of UTXOs. People and organisations who control money in Bitcoin have incentives to use a Bitcoin transaction to join small amounts together into a bigger amount. This can reduce fees if managed carefully. It also diminishes the creation of unspendable dust.
Note that all nodes verify data, it isn't just miners. Other sorts of nodes, such as wallets, do not depend on miners to perform verification and do not need to trust miners. Note that verification is very different from confirmation.
I believe the average computing power (energy) consumed by a miner per block mined is primarily determined by the current difficulty/target. This reflects the total hashpower being applied to the network by all active miners. I believe other factors are relatively insignificant.
The average computing power (energy) consumed by any node per incoming block verified only significantly depends on the number and complexity of transactions in that block. It doesn't depend on the size of blockchain.
how do [Bitcoin nodes] verify/check if earlier blocks were tampered with if not by checking the validity of the entire blockchain?
If you present a node with a new version of an old block, the node will validate it in the usual way. It will presumably have to walk back it's UTXO set using a change log. It knows that prior blocks have already been validated and don't need to be revalidated. It will then assess whether the new chain-head based on that new block has greater work than the existing chain-head based on the potentially replaced block. If the new block is the start of a chain-head with more work then all the blocks in the replaced chain-head are effectively invalidated, including all coins created in transactions in them.
I believe nodes keep track of at least some alternative chain-heads. Presumably both potential replacements and recently replaced. I don't know what criteria they use to discard them (e.g. absence of growth for some threshold time?)
