Daisy's powers are part of her, genetically, they can't be taken from her (although they can be turned off). Nathaniel was able to also acquire her power, by obtaining her DNA and using Whitehall's process to graft it into himself. But he couldn't remove the powers from her the way you'd remove an appendix, the powers are still part of her genetic code. She couldn't use them when she was captured because she'd been drugged.
I would assume the McKenzie Chronicoms maintained the act just in case they were being watched, yes - after all, CCTV in the prison cell is how Mack knew they were there to begin with. And Chronicoms are nothing if not thorough.
This isn't the first time there has been a second time skip within minutes of the first. I guess, just like in 1973, the Chronicoms achieved what they were after extremely quickly! Although...since their time ship was damaged or destroyed, I'm not clear what the Zephyr is now following. I thought it was piggy-backing the Chronicom timeship?
I think it was Mack's parents - we saw the Chronicom giving him the photo back in 1973 and calling it leverage over the SHIELD team. So, yeah, Mack's parents.
Overall, I thought this was the weakest episode of the season so far, and not just because it wasn't as funny - it was also quite disjointed, I felt. I'm thoroughly enjoying the ride of this final season, though, even if I do miss Fitz. I'm loving having Sousa on board, though! In interviews, Gjokaj has said he only has a cameo role in the season - now, three episodes to me seems like more than a cameo, but his statement does imply that he won't be around for the whole season, which is a shame. I think they should keep him, now they have him!