How does the North have any kind of army left at all?

They made a big deal of showing in early seasons how pretty much all the able bodied men were with Robb and his army was slaughtered at the Twins. The Ironborn were able to pretty much walk right in with little resistance. Raising a couple hundred to retake Torrhen's Square or Winterfell was a big deal. And these were the leftovers.

Then they had a civil war and Battle of the Bastards that killed all kinds of people. These were made up primarily of the same Bolton/Karstark men not slaughtered against the paltry number of loyalists that Jon could find. Then the attack on Winterfell by the Army of the Dead. The Umbers were already wiped out before then. Few remaining Mormonts were wiped out during the battle.

On top of that they gave the North a tiny population in the show that's less than the population of KL.

Now they still have men who are willing to march South with Robb to face the Lannisters?

And only half the Dothraki and half the Unsullied were killed in the Battle of Winterfell? WTF? Wasn't it like virtually all of the Dothraki and Unsullied based on what we saw on screen? Was the other half waiting in the mountains?