Is Max in some sort of barely-working-autopilot-mode (like the protagonist in the movie "Click") or does she behave the same as usual, but without time travelling?
I think she behaves the same as she usually would, but subject to whatever changes were affected by what she changed. After going back and changing something, she doesn't remember what she did in the "new timeline" between then and when she "arrives" back in the present. This is pretty clear from scenes like the airplane, and coming back to Chloe on the bluff, where she has to take a minute to re-orient herself.
If she retained any memories in the past during the "in between time", then 13-year-old Max would have had a HUGE lead on what was about to happen 5 years later.
But she can, of course, still hold a poker face. When William spoke about her writing to Chloe, she didn't necessarily remember writing the letters/poems, but she knew that she had radically changed the past, so she kept a straight face about that information to avoid appearing abnormal to what William would have expected.
Or does she indeed use her time travel powers, but not using photos?
I'm not sure what you mean by this. Can she still use her normal rewind power in the alternative timeline she created by a focus rewind, before she "arrives" back in the present? I think the answer to this would be "yes," although I'm not sure there was anything in the game to show it conclusively.
(Note: Max refers to the "jump into a photo rewind" power as "focus rewind" at one point, in her diary entries.)
Or, the real complicated option, can she use photo-time-travel while photo-time-travelling?
Yes, she can. In fact, she does exactly this while escaping from the dark room.
She first wakes up in the dark room after Jefferson is finished shooting her and is preparing to kill her. Then she used focus rewind to jump back and kick the tray, and then returns to the present. This doesn't get her out, but it makes a new photo available to her. She then uses focus rewind on the new photo to jump back to a time while Jefferson is still shooting, and convinces him to give her her diary. While still in that focus rewind moment she uses the same power again to jump back to the classroom where the game began and warn David.