Why are police vans called paddy wagons?

You're on the right track with the Irish connection, but it's not the great numbers of Irish policemen in America who gave the paddy wagon its name. Instead, as one source indicates, it came about because in the late 19th century, when the term was coined, the Irish were often the "low men on the social totem pole," and it was they who were rounded up and placed in the police patrol wagon when a show of power was needed by the police for publicity purposes. Paddy is the diminutive form of Padraig, Irish-Gaelic for `Patrick' and a common first name among the Irish.

Yes, that's exactly what it means. Either of those two possible origins are debated.

I learned about this in criminal justice class but frgot.

I believe it has something to do with the Bow Street Runners.

I dunno lol wiki it..