In this paper, we propose a highly accurate indoor position and direction estimation system using a simple fully connected deep neural network (DNN) model on Bluetooth Low Energy (BLE) Received Signal Strength Indicators (RSSIs). Since the system's ultimate goal is to function as an indoor navigation system, the system estimates the indoor position simultaneously as the direction of movement using BLE RSSI fingerprints recorded indoors. To identify the direction of movement along with the position, we decided to use multiple time instances of RSSI measurements and fed them to a fully-connected DNN. The DNN is configured to output the direction with the location simultaneously. RSSIs are known to be affected by various fluctuating factors in the environment and thus tend to vary widely. To achieve stable positioning, we examine and compare the effects of temporal interpolation and extrapolation as preprocessing of multiple RSSI sequences on the accuracy of the estimated coordinates and direction. We will also examine the number of beacons and their placement patterns required for satisfactory estimation accuracy. These experiments show that the RSSI preprocessing method optimum for practical use is interpolation and that the number and placement of beacons to be installed does affect the estimation accuracy significantly. We showed that there is a minimum number of beacons required to cover the room in which to detect the location if the estimation error is to be minimized, in terms of both location and direction of movement. We were able to achieve location estimation with an estimation error of about 0.33 m, and a movement estimation error of about 10 degrees in our experimental setup, which proves the feasibility of our proposed system. We believe this level of accuracy is one of the highest, even among methods that use RSSI fingerprints.