How can I start android application info screen programmatically?

In 2.2 and below, there is no public APIs you can access. But you can still start the InstalledAppDetails activity just as the ManageApplications does. see here

 // utility method used to start sub activity
 private void startApplicationDetailsActivity() {
     // Create intent to start new activity
     Intent intent = new Intent(Intent.ACTION_VIEW);
     intent.setClass(this, InstalledAppDetails.class);
     intent.putExtra(APP_PKG_NAME, mCurrentPkgName);
     // start new activity to display extended information
     startActivityForResult(intent, INSTALLED_APP_DETAILS);
 }

Conclusion: you can start the “application info” screen like this i wrote:

private static final String SCHEME = "package";

private static final String APP_PKG_NAME_21 = "com.android.settings.ApplicationPkgName";

private static final String APP_PKG_NAME_22 = "pkg";

private static final String APP_DETAILS_PACKAGE_NAME = "com.android.settings";

private static final String APP_DETAILS_CLASS_NAME = "com.android.settings.InstalledAppDetails";

public static void showInstalledAppDetails(Context context, String packageName) {
    Intent intent = new Intent();
    final int apiLevel = Build.VERSION.SDK_INT;
    if (apiLevel >= 9) { // above 2.3
        intent.setAction(Settings.ACTION_APPLICATION_DETAILS_SETTINGS);
        Uri uri = Uri.fromParts(SCHEME, packageName, null);
        intent.setData(uri);
    } else { // below 2.3
        final String appPkgName = (apiLevel == 8 ? APP_PKG_NAME_22
                : APP_PKG_NAME_21);
        intent.setAction(Intent.ACTION_VIEW);
        intent.setClassName(APP_DETAILS_PACKAGE_NAME,
                APP_DETAILS_CLASS_NAME);
        intent.putExtra(appPkgName, packageName);
    }
    context.startActivity(intent);
}