How can I add multiple collection views in a UIViewController in Swift?

This is possible, you just need to add each UICollectionView as a subview, and set the delegate and dataSource to your UIViewController.

Here's a quick example. Assuming you have one UICollectionView working, you should be able to adapt this code to your own uses to add a second fairly easily:

let collectionViewA = UICollectionView()
let collectionViewB = UICollectionView()
let collectionViewAIdentifier = "CollectionViewACell"
let collectionViewBIdentifier = "CollectionViewBCell"

override func viewDidLoad() {
    // Initialize the collection views, set the desired frames
    collectionViewA.delegate = self
    collectionViewB.delegate = self

    collectionViewA.dataSource = self
    collectionViewB.dataSource = self

    self.view.addSubview(collectionViewA)
    self.view.addSubview(collectionViewB)
}

In the cellForItemAtIndexPath delegate function:

func collectionView(collectionView: UICollectionView, cellForItemAtIndexPath indexPath: NSIndexPath) -> UICollectionViewCell {
    if collectionView == self.collectionViewA {
        let cellA = collectionView.dequeueReusableCellWithReuseIdentifier(collectionViewAIdentifier) as UICollectionViewCell

        // Set up cell
        return cellA
    }

    else {
        let cellB = collectionView.dequeueReusableCellWithReuseIdentifier(collectionViewBIdentifier) as UICollectionViewCell

        // ...Set up cell

        return cellB
    }
}

In the numberOfItemsInSection function:

func collectionView(collectionView: UICollectionView, numberOfItemsInSection section: Int) -> Int {
    if collectionView == self.collectionViewA {
        return 0 // Replace with count of your data for collectionViewA
    }

    return 0 // Replace with count of your data for collectionViewB
}

Yes--this is entirely possible. You can either assign their respective UICollectionViewDelegates/UICollectionViewDataSources to different classes or subclass the CollectionViews, assigning both the delegate and data source to your current viewController and downcast your reference to collectionView in the delegation methods like so:

@IBOutlet collectionViewA: CustomCollectionViewA!
@IBOutlet collectionViewB: CustomCollectionViewB!


func collectionView(collectionView: UICollectionView, cellForItemAtIndexPath indexPath: NSIndexPath) -> UICollectionViewCell {

    if let a = collectionView as? CustomCollectionViewA {
        return a.dequeueReusableCellWithIdentifier("reuseIdentifierA", forIndexPath: indexPath)
    } else {
        return collectionView.dequeueReusableCellWithIdentifier("reuseIdentifierB", forIndexPath: indexPath)    
    }
}

Subclass UICollectionView like this:

class CustomCollectionViewA: UICollectionView {
    // add more subclass code as needed
}

class CustomCollectionViewB: UICollectionView {
    // add more subclass code as needed
}