The construction of Cornell BNL Energy-Recovery-Linac Test Accelerator (CBETA) was completed at Cornell University's Wilson Laboratory in 2019. CBETA is designed to accelerate electrons from 6 MeV to 150 MeV in four linac passes using a single Fixed Field Alternating gradient (FFA) return beamline accepting all energies from 42 to 150 MeV. Energy recovery is achieved by decelerating the beam within the Superconducting Radio Frequency (SRF) cavities, in which the beam returns energy to the electromagnetic field. Energy recovery allows CBETA to produce a beam current much higher than with conventional storage rings. This thesis focuses on two important limits of CBETA: the beam current limit due to Beam Breakup (BBU) instability and the bunch charge limit due to Coherent Synchrotron Radiation (CSR) effects. For BBU, elementary theories are revisited to benchmark the simulation codes. Additional theory regarding the scaling law of the threshold current and the effect of chromaticity are also investigated. For CSR, a new "2-bend" theory has been developed by extending the conventional 1-bend theory using the Lienard-Wiechert formula. The new theory is essential to describe CSR wake propagation when magnets are located close to each other, as in CBETA. These new theories could benefit designs and researches of future ERLs. For both topics, extensive simulations have been performed using the software developed by Cornell University, Bmad.