In theory you don't need R2. However in practice, there's always a little bit of DC offset at the input. Without R2, that would cause the output voltage to slowly drift up (or down) until it reached it's maximum (or minimum).
No, not "infinitely" but with the open-loop opam gain Ao (which is 100 dB or even more).
Please keep in mind that each opamp designed to operate in its linear mode needs dc feedback for a stable and suitable bias point.