This work reports new measurements on differential jet shapes and semi-inclusive jet fragmentation functions from Au+Au collisions at $\sqrt{s_\mathrm{NN}}=200$ GeV with the STAR detector at RHIC. The jet shape variable is used to probe the internal jet structure by looking at the radial profile of the most energetic jet (leading jet) of each triggered event. A first study of the differential jet shape at RHIC energies is performed and extended to further include a dependence of the azimuthal angle between the jet and the second-order event plane. This work shows early hints of a possible event-plane dependence of the differential jet shape and motivates further studies. Jet fragmentation functions for 40-60% peripheral Au+Au events are examined via a semi-inclusive approach whereby recoil jets from a high transverse momentum trigger tower are measured and compared to PYTHIA 8 simulations as a vacuum reference. A ratio of the fragmentation functions in Au+Au to PYTHIA 8 shows little to no modification (ratio $\sim 1.0$) within uncertainties across three separate jet transverse momentum bins.