How can I sent my Public Key from DC to somebodys mail address ?
Delta Chat sends your public key automatically in each outgoing message inside the Autocrypt header. Thunderbird supports this header and will offer to import the key at the top of the message. The other popular mail client supporting this specification is K-9 Mail for Android:
There is no option to send the key as an attachment. If you want to do it, you can export the key, import it in Thunderbird and use it to send the key in a more conventional way.