Are we at the point where we can identify what percentage of transactions related to certain industries?
Not really! The percentage of addresses that are tied to known organizations is quite small. You also have to consider that many transfers occur without any change in ownership, that is, a person sends bitcoin from one address they control to another.
I would point out that they are turning away donations. I think the sorts of people that donate BC are probably unlikely to donate if BC is not an option.
However, my biggest suggestion is not to them, but to you: be prepared for the possibility that nothing you say is going to change their mind. Being right is no guarantee that you will be able to ...
Am I right that by implementation everybody with a client is theoretically able to mine?
Yes, it just won't be very effective without dedicated mining hardware.
Would it be possible (without changing half the code base) to limit the right to mine to some charitable groups and giving the other agents just the permission to do transactions?
Yes, you can ...
GiveBTC by the Bitcoin Foundation Canada / Bitcoin Embassy is the best directory I've seen. Linked from the top of that page, they also have an excellent handbook for charities considering accepting bitcoin donations.
I need to know the charitable bitcoin address. I mean that using payment processer, like bitpay, are not useful in my case.
I'm sorry to ...
You customers can exhange any currency to Bitcoin and pay via Bitcoin with no fees.
So, you need to support traditional payment methods and Bitcoin as well, as a new way of payment over Internet. It's the future of payment.
Some day, you will kick-off VISA and Paypal from your website ;)