They did use cartridges... of paper. And with a clean musket 3 shots is doable...
But the exact weapon and exact type of ammo do effect this. Using a springfield with endfield ammo is a bit easier than an enfield with enfield ammo... and naturally doing so when kneeling behind you breastwork under fire is a bit different than doing it on a modern calm firing range...
This youtube movie do cover the two main types pretty well. (1855 and 1861)
And no, the soldiers usually didn't make cartridges... and cartridges was one of the things the south did not lack.
(they made many and also imported many from the UK... and they are a bit different )