This paper studies the dynamics of order positions and related queues in a limit order book (LOB) under a general stochastic setting. The authors derive fluid limits (first-order approximations) for the order position and the best bid/ask queues, showing that the order position decreases at a rate proportional to the mean intensities and average sizes of market and cancellation orders. They also obtain diffusion limits (second-order approximations) for the queues, which converge to a two-dimensional Brownian motion with explicit covariance structure. Using these results, they analyze fluctuations of order positions around their fluid limits, proving that these fluctuations are Gaussian processes with mean-reversion, where the mean-reversion speed depends on order arrival and cancellation rates. The paper provides explicit analytical expressions for key quantities such as expected order execution time, queue depletion times, and tail probabilities via large deviations. The methodology relies on functional strong laws, functional central limit theorems, and convergence of stochastic integrals, and is applicable to various order arrival processes including Poisson and Hawkes processes. These results offer practical insights for algorithmic trading, particularly for valuing order positions and assessing execution risk.