Most existing studies on massive grant-free access, proposed to support massive machine-type communications (mMTC) for the Internet of things (IoT), assume Rayleigh fading and perfect synchronization for simplicity. However, in practice, line-of-sight (LoS) components generally exist, and time and frequency synchronization are usually imperfect. This paper systematically investigates maximum likelihood estimation (MLE)-based device activity detection under Rician fading for massive grant-free access with perfect and imperfect synchronization. We assume that the large-scale fading powers, Rician factors, and normalized LoS components can be estimated offline. We formulate device activity detection in the synchronous case and joint device activity and offset detection in three asynchronous cases (i.e., time, frequency, and time and frequency asynchronous cases) as MLE problems. In the synchronous case, we propose an iterative algorithm to obtain a stationary point of the MLE problem. In each asynchronous case, we propose two iterative algorithms with identical detection performance but different computational complexities. In particular, one is computationally efficient for small ranges of offsets, whereas the other one, relying on fast Fourier transform (FFT) and inverse FFT, is computationally efficient for large ranges of offsets. The proposed algorithms generalize the existing MLE-based methods for Rayleigh fading and perfect synchronization. Numerical results show that the proposed algorithm for the synchronous case can reduce the detection error probability by up to 50.4% at a 78.6% computation time increase, compared to the MLEbased state-of-the-art, and the proposed algorithms for the three asynchronous cases can reduce the detection error probabilities and computation times by up to 65.8% and 92.0%, respectively, compared to the MLE-based state-of-the-arts.