  We study the excitations that emerge upon doping the
translationally-invariant correlated insulating states in magic angle twisted
bilayer graphene at various integer filling factors $\nu$. We identify
parameter regimes where these are associated with skyrmion textures in the spin
or pseudospin degrees of freedom, and explore both short-distance pairing
effects and the formation of long-range ordered skyrmion crystals. We perform a
comprehensive analysis of the pseudospin skyrmions that emerge upon doping
insulators at even $\nu$, delineating the regime in parameter space where these
are the lowest-energy charged excitations by means of self-consistent
Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We
explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key
ingredient behind a recent proposal of skyrmion superconductivity. Building
upon this, we construct hopping models to extract the effective masses of
paired skyrmions, and discuss our findings and their implications for skyrmion
superconductivity in relation to experiments, focusing on the dome-shaped
dependence of the transition temperature on the twist angle. We also
investigate the properties of spin skyrmions about the quantized anomalous Hall
insulator at $\nu=+3$. In both cases, we demonstrate the formation of robust
spin/pseudospin skyrmion crystals upon doping to a finite density away from
integer filling.
