You will need to goto a 3rd party website that hosts Google apps and download the newest (for your device) version. The one I use is http://gappsandroid.blogspot.com/ , you can download EVERY single Official Google app.

Absolutely. You will need to build a mechanism, though, for your app to call home to the server, find out if there's a newer version of the app, and if there is, pull it down and install it. Once you've determined that you do need to pull down an update, you can do that with something similar to this AsyncTask:

protected String doInBackground(String... sUrl) {
    String path = "/sdcard/YourApp.apk";
    try {
        URL url = new URL(sUrl[0]);
        URLConnection connection = url.openConnection();
        connection.connect();

        int fileLength = connection.getContentLength();

        // download the file
        InputStream input = new BufferedInputStream(url.openStream());
        OutputStream output = new FileOutputStream(path);

        byte data[] = new byte[1024];
        long total = 0;
        int count;
        while ((count = input.read(data)) != -1) {
            total += count;
            publishProgress((int) (total * 100 / fileLength));
            output.write(data, 0, count);
        }

        output.flush();
        output.close();
        input.close();
    } catch (Exception e) {
        Log.e("YourApp", "Well that didn't work out so well...");
        Log.e("YourApp", e.getMessage());
    }
    return path;
}

// begin the installation by opening the resulting file
@Override
protected void onPostExecute(String path) {
    Intent i = new Intent();
    i.setAction(Intent.ACTION_VIEW);
    i.setDataAndType(Uri.fromFile(new File(path)), "application/vnd.android.package-archive" );
    Log.d("Lofting", "About to install new .apk");
    this.context.startActivity(i);
}