A good measure for me whether I'm up for a flush is how well my bowels are working. So, if you are having a good bowel movement every day, and you aren't acutely unwell, for example you don't have the flu - then yes I think you can go ahead.
I've never caught my stones before they hit the water - so it will be very interesting to hear how others catch them. For the ones that float, they could be collected by a strainer after you go to the toilet I guess - or you can just estimate how many you've expelled because you can see alot just looking into the toilet with a naked eye, or even better with a torch.
No matter how much you dump in the toilet, it should not cause any problems to your toilet system.