His regret is going to be to do with his father & the relationship they had/didn't have. That & the fact that Jemma wasn't in his life made him into the person we saw in the episode.... but, he still seems to have the drive to protect people close to him and as Aida put herself close to him, his drive is to protect her.
What I got from the episode was his mind joining the dots on it's own was probably more to do with T.A.H.I.T.I. rather than any training
Daisy jacked into the Framework through not official means, which meant that her 'avatar' in the FW was just a program rather than her, the situation she was in (living with Ward) isn't to do with her regrets. if her regrets were affecting the FW, then it would have been Lincoln in the bed IMHO.
Oh God...This one will break people...
Not seen the promo...
I think May is probably more broken than she was at the start of the show, the incident with the kid in RL wrecked her so knowing that the kid wouldn't have killed all the others in the 'Cambridge incident' would completely tear her to pieces. Then HYDRA appears (or already existed publicly) promising to keep people safe from the Inhuman infestation, I could see her joining them and letting herself be run by the rules and order of HYDRA rather than think about her own being (if that makes sense).
Like Daisy, Jemma hacked in, her avatar was doing what AIDA wanted rather than what she would have done. Aida knows that the only way to break Fitz from her control is to get him near Simmons.... and that with FitzSimmons together again, they'd eventually escape to stop her in the Real World... so she had the Avatar of Simmons murdered in the HYDRA uprising to keep Fitz from being able to escape her grasp.