I being very anti-regina, would say no. TBH, I doubt her love for him even now, the TLK they gave him in Season 3 and all. I know that seems like solid proof but I'm admittably bias.
Don't know what episode you are talking about. I think she grew to love him in the twisted way she knew love. I mean she had a terrible mother that showed her "love" via machinations and plotting her child's life.
I think she loved Henry is her twisted way and then grew to discover true (as in the real concept of) love and then truly loved him in season 3a and 3b.
I agree. Regina, pre her reawakening, loved the way a child would. Like a closed fist, she sought to possess what she loved, rather than allowing it to be a free exchange.
Ew! Really bad image there.
The problem with how Regina and Henry's relationship was portrayed throughout the show is that it was not very consistent: in S1 Regina was the villain so, although they showed some of her more human aspects, she was made out to be more of a bad mother; as the show progressed and she was shown in a more sympathetic way, her relationship with Henry was softened, even pre-curse breaking (see In The Name Of The Brother and Save Henry).
I think overall we have to consider two things:
It is also interesting to remember what Mary Margaret said at some point: Henry kind of lost it when he learned he was adopted. Add oncoming pre-puberty, he became rebellious and I think that all combined ended up staining their relationship to the point we saw in S1. If we had to hypotise a timeline it may be like this:
It is also interesting to notice that, while Henry was still cold to her for most of S2, he did care about her (much more than he showed in S1) and actually started believing in her before she did something truly redeeming. Actually, it was Henry believing in her that inspired her to hop on the redemption path. I think that's quite telling of the fact that, before everything went downhill around S1, there was some genuine love between them that allowed Henry to see the good in her and give her a chance, otherwise he would have just jumped ship with the Charmings and never shown any concern with Regina at all (let's face it, he's a selfish kid).