the fastest space vehicle in our solar system is the Parker Solar Probe, a NASA spacecraft launched in 2018 with the primary objective of studying the Sun. The Parker Solar Probe has been designed to get closer to the Sun than any previous mission, and it achieves this by using multiple Venus flybys to gradually decrease its orbital distance.
The Parker Solar Probe is expected to reach speeds of up to 430,000 miles per hour (700,000 kilometers per hour) relative to the Sun. In terms of its speed relative to Earth's orbital velocity around the Sun, it can be a bit more complicated to quantify due to the different orbital paths. However, it is safe to say that the Parker Solar Probe's speed far exceeds Earth's orbital velocity, which is approximately 67,000 miles per hour (107,000 kilometers per hour).
Regarding whether the Parker Solar Probe is traveling beyond our solar system, the answer is no. The primary objective of the mission is to study the Sun and its immediate environment, so the spacecraft remains within the boundaries of our solar system. The Parker Solar Probe's closest approach to the Sun, called perihelion, will bring it within about 4 million miles (6 million kilometers) of the Sun's surface, but it will not venture beyond the boundaries of our solar system.