Can I just see the data/aircraft my receiver is uploading?

This is only available on the website for now.

Yes, you can do that. Here is how you do that: 

1. Go to Filters -> Custom (see image below).

2. Your receiver(s) will automatically show up here. Select your receiver(s) and you will start seeing the aircraft uploaded by that receiver(s) only.

To go back to the normal view, simply uncheck the receiver(s) from the Filters windows.