batch processing - Mass export all images as individual JPEGs in InDesign?

I am new to Indesign. I have a file that contains images with Photoshop clipping paths. I want to export all the clipped images in a folder. I have tried doing the "Copy Links To" and it successfully exported the original images. However, I do not want the original images but the clipped images instead. Is there a way for me to export all the clipped images as JPEG or TIFF and not the original linked image? In short, I want to export the images without their background. I hope I'm making sense. I have about 800-1000 images so a batch processing method would be highly appreciated.

I actually found a way to export the images the way I want them to be. I just need to click the image container (not the image), go to File>Export and then export it as JPEG. In the pop up window, I choose export selection, maximum quality, and 2400 resolution. It exports the images the way I want them to be. But I have to do this one by one. I just have two concerns:

1. 
   

   Is there a way for me to do this by batch? Like select all the image containers and export them one by one automatically?

   
   



2. 
   

   Is there a way to automatically name the saved files according to the original image name?

   
   

Thank you for your help!

Update: I found this script from one of the posts here and modified it a bit to suit my needs. It appears to work in most of my INDD documents, but it fails in others. I wonder why. I sometimes get the error message that

Error string: null is not an object

Source: fileName = File ( rect.graphics[0].itemLink.filePath ).name;

I also noticed that it skips some objects and won't download all of the images. I guess it skips those that are not in rectangles.

test();

function test()
{
var myDoc = app.activeDocument,
apis = myDoc.allPageItems, rect, fileName;

while ( rect = apis.pop() )
{
if ( !(rect instanceof Rectangle) || !rect.graphics[0].isValid ){ continue;}



fileName = File ( rect.graphics[0].itemLink.filePath ).name;
fileName = fileName.replace( /\.[a-z]{2,4}$/i, '.jpg' );


app.jpegExportPreferences.exportResolution = 2400;
app.jpegExportPreferences.jpegQuality = JPEGOptionsQuality.MAXIMUM;


//give it a unique name
var myFile = new File ("C:/Users/RANFacistol-Mata/Desktop/Image Trial/"+ fileName);



rect.exportFile(ExportFormat.JPG, myFile);
}
}

Is there a way for me to modify this script such that instead of iterating through all the rectangles, I would iterate through all of the objects instead, much like clicking this next button

And then check if that object contains an image (jpg, tiff, psd, ai, eps). If it does, then I will export it as scripted above.

Thank you for your help!