Should I not read internet news in the bathroom on my smartphone because of the possibility that an article may come up that mentions the word God or mentions something in a Jewish context? Also, should I not speak on the phone in the bathroom because of the possibility that the person on the phone may say the word God or mention something like Baruch Hashem or Shabbat Shalom?

In regards to news, whether on the smartphone or in a newspaper, there is no prohibition of reading, and it has the advantage of distracting one from thinking Torah thought in the bathroom. If HaShems name comes up it can be ignored, so I would not see that as a worry. On the other hand, conversations while in the toilet, should be avoided. There is a notion of privacy (or tzniut) that suggests that we should not be engaging others in conversation when attending to very private needs. So phone conversations I would avoid. Certainly if one has to engage in such a conversation, one should avoid using HaShem's name in any form, and stay away from divrei Torah ghenerally.