"I need to know if I can use a program to:"
Sure - It's called GPG. :)
"Import a public key file, without connecting to the web"
Sure - gpg --import /path/to/public/key (How that key gets on your file
system is out of scope - Maybe you got it from someone over the internet or
maybe they gave you their key in person or whatever. Either way, once it
exists in your file system go import it.)
"Choose to encrypt a text with a different key;"
Sure - You can encrypt to whatever arbitrary key you want. Use the -u option
when invoking GPG to specify which to use.
"Export my own keys (again never connecting to the web);"
Again, sure. Just like GPG has --import I mentioned earlier, it also has
--export. An example would be gpg --export -a "GNUuser" >
/path/to/save/public/key and you'll then have your ASCII-encoded public key
at that point in your file system. Want to export your secrety key instead?
Replace --export with --export-secret-key. Ta Da!
"Make the whole encryption/unencryption process in my computer"
Yeah - Use GPG to encrypt & decrypt messages. It has -e and -d options for
encrypting and decrypting.
"Protect/hide the keys that I have in my computer;"
Use full-disk encryption?
"Preferably with a GUI;"
There are a number of GUI frontends listed at
http://www.gnupg.org/related_software/frontends.html
So, as you can see, it's all about reading the documentation of GPG, from
which you could have arrived at these same answers instead of me copying &
pasting them for you. :)