Smart Contract Upgrades

How can I detect an upgradable Smart Contract and the Admin who can control it?

And how can I know, if a Smart Contract actually was programmed immutable?

Depending on what type of proxy is being used, you can call different functions and/or read EIP1967 storage slots -- see documentation on proxies. Etherscan also shows if a contract is a proxy (although this may not work in all cases).