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How do space probes find their way, for example, to explore dangerous planets like Jupiter or Saturn that have powerful magnetic fields? Do scientists control it from stations in NASA or they have a built in predefined program?
My second question is, how much fuel do probes (e.g. Voyager 1) use to travel? (Explain its equivalent with car consumption). Are they all powered by their own solar panels?
As to whether space probes are controlled, or follow a predefined program, it's yes to both.
One way to think about trajectory planning is that space probes are like billiard balls. By being very accurate with the initial hit (in spaceflight: the rocket flinging the probe away from Earth), the future course of the billiard ball can be made so it visits several interesting locations as it bounces around (in spaceflight: encounters the gravitational fields of solar system bodies), with no further propulsion needed.
You can, however, bring some rocket propellant along with you. It eats into the mass budget of things you would rather have brought, like scientific instruments. This extra propellant can be used for small adjustments, or bigger stuff like slowing down when arriving at a planet (otherwise you just fly by).
As for how much fuel space probes use to travel, this is hard to answer. For most of the time, they just coast along, using no fuel at all. The only times a spacecraft needs propulsion is when it need to change its velocity. Reading about delta-v budgets would perhaps be enlightening, but really, no meaningful comparison with car consumption can be made.
Finally, yes, solar panels is the most common way to get power onboard. Other options include 1) Just bringing batteries and run on them until they are empty (short missions) and 2) Bringing an RTG, a small piece of radioactive material giving off some heat and electricity.
Keep in mind that propulsion changing the velocity and course of a spacecraft is completely separate from powering equipment, like cameras and computers, onboard.
To elaborate on fuel consumption: Space is mostly empty, there is almost nothing to slow you down. Vehicles on Earth constantly have to fight against friction and air resistance. In contrast a space probe launched at several kilometers per second will just keep going and will only change its speed or deviate from its course if gravity acts on it (or if it hits something, even if it’s just light). For example because it comes close to a planet. If the probe wants to change its course it has to fire its thrusters which basically work by throwing stuff (expanding gasses or accelerated ions) out the back as fast as possible. There is nothing to “push” against, so something like wheels or propellers simply can’t work.
Remember that orbiting objects (e.g. artificial satellites orbiting the Earth) travel at several kilometers per second and can do so basically indefinitely without expending any fuel as long as they are high enough up to not encounter any stray atmosphere.
Edit: As for how much fuel is required: You really need the Rocket Equation for that. It basically depends on how efficient (Isp) your engines are and how much of your rocket’s mass is propellant. For rockets launching into Low Earth Orbit it’s not rare that 90% of the launch mass is just propellant. For example a Falcon 9 is 549t at launch, weighs ~30t when empty and can only put 22.8t into Low Earth Orbit. All of that only to get through the Earth’s atmosphere and achieve 7.5km/s delta-v.
A few words on navigation.
Midflight, the navigation is done on earth. The deep space network can with very high precision calculate:
In effect: direction, distance and speed allows us on earth to calculate any necessary orbit changes compared to where we want the probe to go.
The probe gets a command, something like: align your spacecraft towards a specific point (using its star finder telescope), light the propulsion engine for x seconds.
To answer the question on navigation, the Deep Space network allows ground crews to monitor those craft constantly. If there are issues with navigation, ground crews can send commands to order the guidance systems to change course. Crafts typically have some sort of telemetry and sensors to maintain course.
With regards to fuel, most of the fuel is burned during launch and separation. On deep space missions, the craft pick up speed via gravity assists from other planets along the way. So essentially these crafts mainly consume fuel for on-board systems as opposed to actually thrust. The Voyagers have isotopes on board that are powering systems. However, Deep Space 1 was the first deep space craft to use an ion engine to build thrust during its mission. It carried about 250 lbs. of hydrazine and xenon to fuel its thrusters.
