Sure. The tracks of all current satellites and most space junk (anything big enough to be picked up on ground-based radar or telescopes) are known. NORAD publishes (as often as weekly) a set of data which, when processed by a simple orbit prediction model, will tell you with fair accuracy where the subject satellite will be in its orbit at any given moment in the near future. And NORAD also maintains a catalog of orbital objects.
The information is out there. Mission ops and planners have expertise, experience, and scads of tools to do this very thing.
There are lots of organizations that will say “no, you can’t.” For starters, you have to comply with ITAR regulations, enforced by various Federal agencies. If your satellite has a radio, it needs to comply with FCC requirements. If it has a camera, you need to talk to NOAA.
Now, you might still say “what if I ignore all of that?” This might actually work if you’re a pariah nation like North Korea and have your own rocket program. But if you’re anyone else, launch providers won’t talk to you unless you comply with the necessary regulations. To some extent, you could probably get away with lying about the capabilities of your satellite, but if you do that I’d hope you have a good lawyer.
Sure you can. Cubesats do it all the time. In fact, an omnidirectional “beep beep” is a requirement. And usually they have no maneuvering capability and so stay up until air resistance brings them down. Granted, this is usually pretty quick since they’re in LEO. And they have to broadcast on specific frequencies and have an FCC license. But still, satellites can be quite simple indeed (though you’re right that it’s only polite to have some plan for deorbiting at the end of mission).