Then I tried getting a wallet for BTC, I downloaded bitcoin core and generated several receiving addresses. What I notices is unlike ETH address BTC don't have a password and seems like no way no access the address on other computers. no password was requested for each address.
ETH is different from BTC. But if you like your wallet file to be encrypted, go to Settings>Encrypt wallet. It just encrypts your wallet file such that no one will be able to use your private keys without the password.
Is it necessary to have a wallet to get the funds on the address?
No. If you have a valid address, you can send the funds to it. You will need a corresponding private key to spend it though.
Is it possible to migrate wallet from 1 PC to another or to an android/apple device?
Yes. You can obtain the wallet.dat and it will contain everything you need, your private keys or master private key. The compatibility of the master private key depends on which client you are using.
What will happen if my PC crashed and needs to be replaced is there a way to retrieve my wallet bec it seems that the data is saved on the PC itself.
How does the system determine that the wallet belongs to me? based on how I understand it the address doesn't belong to me but it is with the wallet.
You just need the wallet.dat to have your private keys back.
The way Bitcoin works is that you have a signature with every transaction that you create. The signature is also used to verify that you have the rights to spend the inputs (UTXO) that is in your address. For example, if you have a few inputs in address X, your client will create the transaction and sign it using your private key while also including the public key. On the network, nodes will be able to use the public key to verify that you indeed own that address and have the rights to spend the Bitcoin. ECDSA allows the signature to be verified against a public key.
Your wallet is merely a tool for you to spend Bitcoins, not to store Bitcoins. The transactions are stored on the blockchain. As long as you have the keys to address A, you can spend the coins in address A.
If you use a desktop client, all you need is the private key to spend it.