I don't know about the symbol but for the "black and white radial" I am assuming you are speaking of the gradient?

Just select whatever you want filled with a gradient, then click on the "black and white radial" swatch. Open your Gradients palette and you will see a large view of your gradient swatch and below will be the gradient in a bar, black to white (or vice versa). At each end of this bar, just below the bar, will be a swatch, one white and one black. Drag any colors you want from your swatches onto this bar to add colors or onto the black and white swatches to replace them. To get rid of a swatch from the gradient, just click and drag it off the palette.

When you've got your gradient the way you like it, click on the large swatch in the Gradient palette and drag it to your swatches palette.

Hopefuly this was helpful and/or not something you already know. :")

--Kara

"I can create a symbol and save it temporarily into symbols file, but when I close the project and start a new one, it's gone.????? Why? "

Because symbols are the work of the Devil and must be banished!

Just kidding, spot colors, symbols, patterns etc. that you create in a specfic document are just saved in that document and aren't made a part of the illustrator as a whole. When you open a new document, illustrator just refers to the default file settings and starts you off from scratch. If you want to make it a regular part of every illustrator file you create, then go to your illustrator/presets/symbols folder and open the Default_CMYK.ai file. Add the symbol to that file and save. Now the symbol should be included in your symbol palette in any new document you make.

Easy Peasy.
Open your new document.
Go to Window>Symbol Libraries>Other libraries...
A finder window will open.
Click on the file with the symbols you created.
Voila. The symbols will open in your new document.