Lots of questions Little Einstein!
We perhaps couldn’t have satellite hovering above the same place on Jupiter – not unless it was far away – it would be really hard. But we could send something to orbit Jupiter.
Jupiter has been used in the past to “sling-shot” spacecraft further out to space, so we certainly could send something to orbit it too!
In a way satellites are programmed probes – we can command them but they usually run autonomously, so we could send them to orbit round Jupiter. We could send a satellite with lots of little probes that could be sent down into Jupiter. They wouldn’t last very long before being crushed by the huge amount of pressure but they might be able to send back some cool pictures before they died.