All those eyes and MC being at the "center of attention", it's the gods. At this point they obessively try to keep their eyes on MC whenever they can.
Spoiler!
MC created a barrier on the 60th floor to block out the G**'s and they can't penetrate it at all. That's why he mentioned how did he live with that pressure, alluding to before in the earlier floors when the gods would always be watching to see what he does. MC at this point is extremely powerful(incalcuably strong) and basically has an antagonistic relationship with the gods hence he's on watch whenever he steps outside the barrier 24/7.
That ice queen is part of the 61st floor whom after some events became friendly with MC. The girl in question she mentioned MC decided to wait on is Lee Yeon Hee. He's waiting for her to beat floor 17 and climb up to where MC is on the 60th floor so that he can continue and "beat" floor 61 as it is impossible by himself(mechanically, not because he isn't strong enough).
