Hi Shradda, don't just create one bulky program consuming all those API's. Instead, create a module for consuming and processing the data of each one separately. This will make it easier to keep your project maintainable.
If Facebook, Instagram, Linkedin and Youtube all provide API's which you can integrate too then yes this would be possible to make.
I believe all those sites have APIs so it should be possible to integrate with Mendix. You’ll have to look at signing up to their developer programmes and agree to their terms and conditions regarding data use.
I would look to handle the API integration using scheduled events if possible. This will periodically load your update data in the background and help keep the Mendix application fast and responsive.