at the end of the relationship, i wanted her to change her life and do something better than this.

That's not your business.

i get in touch with her sister. told her about her sister's job, about her financial problems, illness(leukemia) and asked for help

While that was a shitty thing to do to someone, it wasn't obviously illegal, as you weren't threatening to disclose private information in return for something. You just disclosed it.

If you don't restore my reputation with my sister and you do not give me 1000$ i sue you

This isn't blackmail either. It's a settlement offer. Your former friend believes she has a civil case she could bring to court - I suspect incorrectly, but I'm not intimately familiar with Italian law on the subject - and is willing to accept a $1,000 settlement in lieu of a lawsuit.

Your options:

• Take the settlement, pay $1,000, and do what you can to patch things up with her sister.
• Negotiate.
• Ignore her and see if she sues. I'd be surprised if she did, as the effort of suing you in Italy would be impressive, and I'd be somewhat surprised if Russian courts had any jurisdiction over a resident in Italy without ties to Russia.