Considering the time-varying K-user single-antenna interference channel (IC), it has been shown that, when terminals have perfect global channel state information (CSI) and they can tolerate asymptotically long delay, applying an ergodic interference alignment (EIA) scheme can achieve half of the interference-free achievable rate. However, in practice obtaining such CSI is challenging, and only a limited delay is acceptable. This paper addresses data transmission over the IC by taking these concerns into account. Specifically, we consider the case that each transmitter attains only quantized CSI via limited feedback signals. This causes imperfect interference alignment and a degraded performance. We propose adaptive schemes to compensate the impact of the CSI uncertainties. We first study a power control problem which concerns how to communicate at fixed rates using minimum transmit powers. A power control algorithm is used to reach the solution. Next, we address a throughput maximization problem when the transmit powers are fixed. Through the analysis of system outage probability, we propose a rate adaptation scheme to maximize throughput. Finally, we quantify the throughput loss in delay-limited systems. Our results show that, even with limited feedback, performing the EIA scheme with proper power control or rate adaptation strategies can still outperform conventional orthogonal transmission approaches.