Currently Bitcoin transactions can take around 45 minutes.
This is not true. Bitcoin transaction is broadcasted instantly. Confirmation time depends on fee rate used, demand for block space, mining pools and few other things. It can take few seconds to few days for a bitcoin transaction to be included in a block. For example: Right now if you use fee rate 1 sat/Byte it will not be correct to expect transaction to be confirmed in few minutes based on https://mempool.space
If everyone in the world uses Bitcoin, computers would have to consume 1000 of terabytes per Hour.
I am not sure what is this calculation based on.
The solution is the Lightning network, which takes transactions Off the Blockchain and groups many transactions into one.
Yes, lightning transactions are off-chain except opening and closing channels require on-chain transactions.
However would taking transactions off the blockchain temporarily, defeat the whole purpose of having ledger transaction?
No. Lightning Network depends on Bitcoin protocol and blockchain. It leverages the security of the underlying blockchain as an arbitration layer.
Consider Orange sphere is Bitcoin and Outer hemisphere is Lightning Network. Layers exist in other things too. Examples: Network Layers, Onion Routing, etc.
Additionally, can Lightning Network know who owns how many bitcoins with multi transactions off the ledger?
The contents of a channel are only known by the two involved nodes. There are two types of channels: Public and Private. Private channels are never advertised. Users can open private channels to a few big liquidity providers, and never advertise a single channel to the rest of the network. The node itself might not even be known to the network. There are few privacy issues with Lightning Network but I am not the best person to comment on it.
Related Q&A: How much privacy does Lightning actually have?
Few links to learn and discuss more about Lightning: