The important part of the blockchain is the unspent outputs, and there is a limit to how large this can get due to the limited number of bitcoin and the smallest allowable fraction of a bitcoin (satoshi).
No, because you can create and spend zero satoshis. Then, amount is sum-neutral, but signatures and scripts are still verified.
There is also a technical limit as to how large the blockchain can be as a function of the block number, as each block has a maximum size.
The number of blocks is unlimited. And if they are deterministic, then you can create a very large chain, which will take a very little space. And because the block number is expressed as a "big number", then it is a much larger limit, than the maximum size of the message, which can go through SHA-256.