Can I use my custom icon with Google +1 or I'm obliged to use one of the icons provided by Google? If I can, how?
Thanks.
I don't think you can since the +1 API is not public (at the time of writing this).
You can however configure the button looks here:
http://www.google.com/webmasters/+1/button/
Also, you can try to figure out the +1 script and see if you can hack something: