Does every node or computer keep track of all of every user's transactions every single dollar as a separate unit or do they group together units in transactions? (eg. transfer of 5 dollars would be looked as one transaction or 5 different ones) Additionally, if every server records all user transactions ever, isn't there a space limit?
These are broad questions. Let me try and answer as simple as possible.
First of all, bitcoin's an ethereum's accounting models are different:
- BTC uses an UTXO based accounting. The user spends what's called an unspent transaction output (UTXO). The balance for an account is the sum of all the UTXOs that account can spend.
- ETH uses an account based account system. The user spends from the balance they have available in an account.
You can read here about the differences and pros/cons of these accounting models.
The minimum accounting units (the cents equivalent in USD) are:
- Satoshis for bitcoin, where a satoshi represents 1 * 10 ^ -8 BTC
- Wei for ethereum, where 1 wei represents 1 * 10 ^ -18 ETH.
You can't transfer less than that minimum unit.
Regarding space, yes, there are theoretical limits, and that's why there are transaction fees - to put a cost on the space and computation costs required to secure the network.