Bandlimiting and OFDM spectrum - what is considered "bandlimited"?
This isn't a question specific to OFDM:

All transmissions need to be bandlimited by law. Hence, law defines band-limited here.

Typically, this happens in the shape of spectrum masks (often expressed in textual form in regulations); these say something like (this is just an example, actual legislation varies across regions and is definitely different):

"not more than -40 dBm/Hz within 10 MHz of the carrier frequency, not more than -90 dBm/Hz between 10 and 20 MHz of the carrier frequency, and -120 dBm/Hz more than 20 MHz away"

Regarding the specialties of OFDM:

You indeed can't pulse shape OFDM without losing its benefits. (You can do a bit of a tradeoff, and trade a bit of orthogonality for out-of-band radiation suppression, but you'd typically avoid that)

That's why you typically have "empty" carriers at the edges. You simply leave room for the sinc to decrease.