Yes, it is true that the eighth doctor claimed to be half human. I will remind you that the same post-regeneration psychosis prompted the sixth doctor to accuse his companion of being a fairy. Don't trust anything a timelord says within 48 hours of regeneration.
Time was only able to move when River Song and the doctor were in physical contact, because it was an intervention in their interactions in the real universe that broke time in the first place. He snogged her because that was the only way he knew she couldn't resist being in physical contact with her which could also be shown on the BBC in that time slot.
Sherlock, because he is a time lord.