Panel 1
Ryoko: Please acknowledge!
Girl: Papa
(note: there is a particular meaning of ninchi in this context. Basically it means for a man and woman who are not married to recognize a child as their own, which then follows with the procedure of recording the child into the family registers. Ryoko is asking Kyon to acknowledge the kid as their own.)

Panel 2
Ryoko: I tried reconstructing a wedding dress but... how does it look?
After having a child out of wedlock, they are now having a wedding... is what this means

Panel 3
picture of the family

Panel 4
Ryoko: I'm just heating it up, so wait just a minute.

Panel 5
Happy dinner time

Panel 6
Bath time

Panel 7
They're playing Old Maid, and Kyon is left with the odd card out, meaning that he lost. Just a side note, but they play the same game in episode 6, when Kyon has to go buy everyone drinks after losing.

Panel 8
Ryoko: Ne, Papa, kiss me
(ahh, the husband and wife are going to get all lovey-dovey)

Panel 9
But it turns out the daughter gets in the way and is sleeping with them.

Panel 10
Kyon: In the end... spent the whole night here...
(Probably referring to his daughter, who's still in bed)

Panel 11
Kyoko: Ahh, good morning! Did you sleep well last night?

Panel 12
Kyon: I'm getting carried away with this... aren't I...
(The meaning of nagasareru here is to get caught up in or get used to someone else's flow, someone else's idea, some development of events, etc. I don't know the context of this comic, but you could assume he's getting swept away by the married lifestyle.)