Would it be okay for me to contact my internship mentor from my last internship asking for any referrals and to suggest me any places where I could apply for an assessment internship? He was quite impressed with my work during my internship and i believe I made a good impression on him, but I am unsure whether this would be a right move or not.

Why not ask him for a second round? Assessments (and PPOs) are often the result of multiple internships at the same firm.

This was an In-House Internship and they made it pretty clear that they don't hire freshers. But the Legal Team was pretty decent sized and regularly used to interact with various firms as they had engaged them for various matters. So I just assumed that even though they might not hire me right now, a recommendation from someone who's a senior in the legal department wouldn't hurt right?