Although is Obama personally Tweeting? eg John Key also had a twitter account, but I don't think he did much or any tweeting himself. I didn't think Presidents had access to mobile internet devices, although maybe that has changed?
No idea. It appears to be a one-way PR style stream rather than an avenue for two-way conversation, which is exactly how John Key ran his.
Trump, on the other hand, uses his as a platform for his bullying. I can't imagine this will be allowed when he's POTUS. But then again I thought it would stop when he became PEOTUS.