Quenched kinetic energy dominated over by on-site Coulomb interactions in the flat band presents twisted bilayer graphene as an exceptional platform to explore correlated phenomena. The emergence of superconductivity in such a system with slow velocity and small carrier density, is particularly interesting yet appears to be paradoxical under the framework of the conventional BCS theory. In the first part of my talk, I will demonstrate that, the dominating quantum geometric contribution to the superfluid stiffness resolves the paradox, and the band velocity constitutes a new limiting mechanism for the critical current analogous to a relativistic superfluid. At denominator 3 fractional fillings, Coulomb interactions and the Wannier orbital shapes are predicted to strongly constrain spatial charge ordering, leading to geometrically frustrated ground states that produce a new class of correlated insulators. In the second part of my talk, I will demonstrate the observation of dominant denominator 3 fractional filling insulating states, and the magnetic ordering signatures and tripled unit cell reconstruction these states display.