can I create a valid address (without private key and public key) with a specific string?
Yes. Do this:
1. Start the address with the valid character (1 for P2PKH, 3 for P2SH)
2. Avoid invalid characters (0OIl) in the string you are using
3. Your string has to be small enough to not exceed the standard address length (160 bit hash when decoded)
4. Convert your string to bytes and pad it with zeros until it is 160 bits
5. Encode the result using Base58check
I want to put everlasting address into blockchain by moving there some dust.
Please don't, you would be creating an unspendable UTXO that will remain in the UTXO set forever. Use OP_RETURN if you want to insert an arbitrary message into the chain...