Time delayed reservoir computing (RC) is a novel artificial neural network that is easy to implement in hardware due to its extremely simple structure. Because of its time-division multiplexed information processing, laser-based photonic time-delayed RCs usually realize parallel processing with polarization/wavelength multiplexing. However, the performance of two different tasks is difficult to regulate separately and simultaneously in the time delayed RC system, especially for the chip-scale configuration. Here, we propose a feedback-free RC system based on a spin-polarized vertical-cavity surface-emitting semiconductor laser (VCSEL), which simplifies the whole system structure and can process time series prediction and waveform recognition tasks in parallel, with employing the input and output coding to provide the effect from past states. By separately setting the number of past states introduced by the coding for the two tasks, the performance of the two tasks can be adjusted respectively. Furthermore, by appropriately tuning the pump polarization ellipticity which is the unique feature for the spin-polarized VCSEL, the computational ability of the proposed RC can be focused on one of the two parallel tasks. Therefore, the proposed RC system is capable of dealing with different tasks with high performance, and also expected to provide a viable solution for integrated neuromorphic computing systems due to its compact, feedback-free structure.