I joined the Stormcloaks but never had gone to Markarth before. During the questline I had to go to Markarth and saw the murder, but I basically ignored it. Also I never got the note from the guy.

Now the Stormcloak campaign is over and I wondering if I can still do the Forsword quest. I didn't get the note, and Markarth is ruled by the Stormcloaks now.

On a side note I never enter Solitude before either, the first time I entered was during the battle. So does that mean that one gatekeeper doesn't get beheaded or was it done and I just don't know about it?

Thanks.

For the Forsworn quest, I suggest you go to the Shrine of Talos and find Eltrys, see if he has the "Look, a letter, I think you dropped it." or similar dialogue option.
Maybe just talking to him can make the quest start, since talking to him at the shrine is the first stage of the quest. I'm not completely sure.

If you're on PC, you could start the quest via console.

Edit:

It seems that you can't complete it after the Stormcloaks questline if you started it (read the note) but did not meet with Eltrys. Since you didn't receive the note, I think you still might be able to do it.