Buddha referring to himself
Please see this question and the selected answer for it which is based on SN 1.25.

The Buddha sometimes referred to himself as "I" and this is not out of conceit or self view, but because he is simply using conventional language.

Why does he refer to himself in the third person as Tathagatha - "firmly established in reality"?

The way I see it, this is just like me talking about humans - "the human eats when he is hungry".  Similarly, the Buddha describes his nature as one who is firmly established in reality, by speaking of the Tathagata in the third person.