yes, there are space-crafts monitoring all planets in our solar system(and possibly beyond).
Galileo
No, Galileo has been the only probe to actually orbit Jupiter.
The optimal trajectory for a spacecraft to perform a Hohmann transfer to Jupiter involves launching the spacecraft from Earth at a specific time and angle to intersect with Jupiter's orbit. This transfer orbit minimizes fuel usage and travel time by taking advantage of the gravitational pull of both Earth and Jupiter. The spacecraft will follow an elliptical path, with a periapsis at Earth's orbit and an apoapsis at Jupiter's orbit, allowing it to rendezvous with Jupiter efficiently.
Yes, NASA's Juno spacecraft is currently in orbit around Jupiter, studying the planet's composition, gravity field, magnetic field, and polar magnetosphere. Juno launched in 2011 and arrived at Jupiter in 2016.
Jupiter's atmosphere is made up of dense clouds of gas that make it challenging for spacecraft to land on its surface. Additionally, the intense radiation and magnetic fields around Jupiter pose risks to the spacecraft's electronic components. It is more feasible and safer for spacecraft to study Jupiter from orbit rather than attempting to land on its surface.
Despite antenna problems, Galileo conducted the first asteroid flyby, discovered the first asteroid moon, was the first spacecraft to orbit Jupiter, and launched the first probe into Jupiter's atmosphere.
No human has ever visited Jupiter. NASA's Juno spacecraft is currently exploring Jupiter and sending back valuable data, but sending a crewed mission to Jupiter is currently beyond our technological capabilities.
The Galileo spacecraft was launched to Jupiter to study it and its moons, and reached it on December 7th 1995. It orbited Jupiter and took measurements of its moon via flybys till September 21, 2003. It did not land anywhere, it orbited Jupiter for the entire time, until it was decommissioned and flew into Jupiter, where it was destroyed.
It's Pioneer 10, launched in March 1972. Pioneer 10 first explored the asteroid belt, then moved on to Jupiter. After that, it explored other outer planets and eventually went outside of the solar system, thus becoming the first spacecraft to flay past Pluto.
Notable missions to Jupiter include the Galileo spacecraft, which orbited the planet from 1995 to 2003, and the Juno spacecraft, which has been studying Jupiter since entering orbit in 2016. The Pioneer 10 and 11 missions and the Voyager 1 and 2 missions also conducted flybys of Jupiter in the 1970s. Additionally, the Hubble Space Telescope has provided valuable observations of Jupiter from its orbit around Earth.
Some examples of satellites or robots that have been sent to Jupiter include NASA's Juno spacecraft, which has been in orbit around Jupiter since 2016, and the Galileo spacecraft, which orbited Jupiter from 1995 to 2003. Additionally, the European Space Agency's JUICE (JUpiter ICy moons Explorer) mission is planned to launch in 2022 to study Jupiter and its moons.
Galileo was the first spacecraft to visit Jupiter.