Save token id into a database in Swift
This:

var token = NSString(format: "%@", deviceToken)
token = token.stringByReplacingOccurrencesOfString("&lt;", withString: "")
token = token.stringByReplacingOccurrencesOfString("&gt;", withString: "")
token = token.stringByReplacingOccurrencesOfString(" ", withString: "")


is actually a bad method to convert an NSData object to an NSString
(containing the bytes in hexadecimal). It relies on description
having the format

&lt;01020304 05060708 090a0b0c 0d0e0f10&gt;


which is not officially documented. In most cases, the description of
an object is only suitable for debugging purposes, but not for further
processing.

I would convert all data bytes explicitly to create the string. Here is a possible implementation as an NSData extension method:

extension NSData {
    func hexString() -&gt; String {
        // "Array" of all bytes:
        let bytes = UnsafeBufferPointer&lt;UInt8&gt;(start: UnsafePointer(self.bytes), count:self.length)
        // Array of hex strings, one for each byte:
        let hexBytes = map(bytes) { String(format: "%02hhx", $0) }
        // Concatenate all hex strings:
        return "".join(hexBytes)
    }
}


which can be used as

let token = deviceToken.hexString()




With 

dispatch_async(dispatch_get_main_queue(), { ... }


you dispatch the URL request to the main queue where it blocks the
UI. You can use dispatch_get_global_queue() instead to dispatch
it to a background thread, or simply use sendAsynchronousRequest():

NSURLConnection.sendAsynchronousRequest(request, queue: NSOperationQueue.mainQueue()) {
    (response, data, error) -&gt; Void in

    if data != nil {
        println("data: \(data)")
    } else {
        println("failed: \(error.localizedDescription)")
    }
}


Now the request is done in the background and then the completion
handler called on the main thread.

In the case of an connection problem, the completion handler is called
with data == nil and error != nil containing information about the
problem.




  shall I use an api key (not sure is the correct word) to "identify" the user


This question is a bit broad and depends on what you are trying to 
achieve. Here are some comparisons of the available methods:


CFUUID Vs. advertisingIdentifier Vs. identifierForVendor
The Developer’s Guide to Unique Identifiers


which might serve as a starting point for your further research.