If they feel they have a case, in which I would say that they do. You are best not fighting them unless you have a vast amount of funds to spare on legal costs. You may succed if you can find an angle, but I would not fight it. Does the site bring in a nice amount of income every month? If you think that the site is worth fighting for then try your best.
Furthermore, since you have publically posted the email, it can theirfore become breach of confidentiality, and you can become liable.
for me you didn't violate anything. I visit your site and no logo's are copied from facebook and you have good adds, so nothing to worry and I think you pick the right name.
Just for your info take a look at this LINK You got company You have people to discuss your problems with.
the word "facebook" has its meaning before Facebook the company came along. Facebook the company provides online forum, social networking, service. Traditional word "facebook" refers to a book with alumni pictures writings... so unless the OP is providing service that is totally different from what Facebook the company is providing, OP does infringe trademark... if OP is selling books, or cosmetic guide.. or anything else.. it will be fine. The keyword is "confusion".. unless you have money to argue the fine point.. very difficult to win in your case
Bidbody, from the looks of your footer, you are not too keen with laws. I might say you might want to deltew your names in your sig too!