It is a local wallet? So it can't be controlled by companies or possibilities to froze funds until KYC approvation?
This will only happen if you keep funds on an Exchange, such as Coinbase (or its custodial Wallet).
Custodial wallets aren't really a wallet, it is an exchange that keep your funds. They can enforce KYC or anything else, as they are the true owners of your bitcoins, as they hodl the private keys.
You will be safe with the wallets suggested by BitMaxz. Just note down the Seed (12-24 words), because that seed contains your private keys.
How with Electrum is possible to use every feature without downloading the blockchain?
Because it is a light weight wallet (SPV). It doesn`t download all transactions in history, just the ones related to your funds.
SPV wallets check balances using explorers such as blockchain.com. Just paste your public address there (used to receive funds) and you can see all its past transactions.
Is it stored on "a" server? If the server go offline I can't use my wallet?
AFAIK, there is no risky of this to happen. If Electrum ever stop working, you can just import your SEED (that words i said) into any other wallet and you will have your bitcoins.