Morse is basically an alphabet, but with dots and dashes instead of letters and digits.
Binary is base 2, 1's and 0's, what computers use at their core (1 and 0 comes from electricity, current flows, current doesn't flow)
Hex is base 16, which is 0,1,2...,9,A,B,C,D,E,F. This base was chosen because it's a multiplier of 2 and big numbers calculations can be done easier then in base 10.
In other words, none of the above are communication methods. You can chose morse as alphabet to tell somebody something, but you still need a method to communicate (letter, email, shouting, etc).
For base 16 / Hex you can take a look at this
ASCII to see how computers interpret numbers as characters.
What's used for safe communication nowadays would be RSA encryption. A pair of keys is generated, public and private key. Public key is shared with everyone who wants
to talk to you. They write the message and before it's sent, message is encrypted with public key. Nobody can see the real message, unless they have the private key.
Private key, as the name implies is only for you, not shared, so only you can decrypt the message successfully.
This is what's used by SSH, HTTPS, OpenVPN, etc
TIP
It's said that base 10 is the one we use (we count from 0 to 9, 10 digits), because we have 10 fingers and makes more sense to do calculations in this way.