Fast radio bursts (FRBs) are transient radio bursts of extragalactic origin characterized by millisecond durations and high luminosities. We report on observations of FRB 20240114A conducted with the Robert C. Byrd Green Bank Telescope at frequencies ranging from 720 to 920MHz. A total of 437 bursts were detected, with a single observation recording 365 bursts over 1.38hr, corresponding to a burst rate of 264 bursts per hour. The average rotation measures (RMs) were 347.0+/-1.0rad/m2 on 2024-Feb-23, and 353.7+/-0.6rad/m2 on 2024-Mar-01. Of the 301 bursts with detected RMs, 81% have a linear polarization fraction greater than 90%, and 14% exhibit circular polarization with a signal-to-noise ratio >5. Our sample also displayed polarization angle swings. We compared the linear polarization fraction of FRB 20240114A with those of the repeating sources FRB 20201124A and FRB 20220912A. Our analysis reveals that all three exhibit similar distributions in both linear and circular polarization fractions. These results indicate that the three sources share the same radiation mechanism. We analyze the fluence and waiting-time distributions of FRB 20240114A, revealing a right-skewed fluence distribution and a bimodal waiting-time structure, suggesting intrinsic emission timescales and potential multiple burst populations. Additionally, we present a novel method to determine the frequency range of bursts based on their spectral characteristics. This algorithm is independent of spectral models and remains unaffected by the removal of interference-affected channels in the data, ensuring robust performance.