No, if you need to load from this information you need the piece you want to use and a proof that that information belongs in the hash stored in the contract. A common way of doing this is using Merkle Trees and it’s variants.
The difference is the cost of storage vs the cost of the proof.
Smart contracts are not aware of transactions, only about calls to them. So probably your notion on how things work is not correct.
Not possible. There is this research of Sharding, on ETH2.0, and Plasma chain, that would be probably what you are looking for.
Plasma is like a subchain with an authority but participants are trustless to leave, it is as you mention only a hash, which uses that merkle trees I mention in very fancy ways. No, in this case transactions are not recorded inchain, they are part of the subchain, which would have its own ledger.