Can the followers of Vadakalai sampradayam recite 3000 Padi Guruparampara prabavam of Brahmatantra Jeeyar? What is the difference between this and 6000 Padi Guruparampara prabhavam?

Yes, Vadakalayars can recite Brahmatantra Jeeyar’s 3000 padi.
6000 padi of Thirukurugai Piran Pillan is common to both the sub sects but particularly 3000 padi of Brahmatantra Jeeyar is recited at Parakala Mutt, and Eduvyakhyanam is recited at Sri Mutt.
Notes:
The expositions that are in tune with Desika Sampradyam can definitely be recited.