Is it possible to save only the hash on the blockchain and the rest on a cloud?
A hash of some data can serve as a proof the data exists, but the data itself won't be available to someone who just has the hash. If you store a hash on some server ('the cloud'), only those with access to the server will have access to the data.
If the server went offline or became corrupted for any reason, users would suddenly become unable to verify transactions. As a user this is terrible: you must fully trust that the server will remain online. So why add a blockchain to the mix? The inefficiency of a blockchain is made tenable by the lack of trust required in a third party when interacting with the system. Storing pertinent info on a centralized server is the opposite of this.
If I save the hash of the data on the Blockchain, is the data still as sa(f)e as saving all the data on the Blockchain?
I don't know what you mean by 'safe', but generally a blockchain is a terribly inefficient place to store arbitrary data.
What else than saving storage is the difference between saving only the hash and saving all the data on the Blockchain?
A hash can prove that some data existed at a certain point in time, but what that data is will be unknown. Only in light of the full data can the hash be verified to be a proof of the data's existence.
For example: with bitcoin transactions we need to know the full data of the transaction, or else how can we know that the transaction is valid? (spends valid inputs, with valid signatures). A hash of the transaction data is not sufficient to determine this.
Is it possible to create the smart contract on a cloud and save the hash on the blockchain?
This question feels confused - a 'smart contract' generally refers to some code that will execute, without trust in a third party. If you must depend on some server to store and execute the code, it isn't really what would be called a 'smart contract'.
Does this have any disadvantage? Will the transactions still be recorded as sa(f)e as on the blockchain?
Huge disadvantage: users will need to trust a centralized server ('the cloud') in order to interact with the blockchain. This means the system will have the worst of both worlds: a heavy trust requirement, and an inefficient blockchain architecture.
