System and planet sizes distances seem enormous. How possible or impossible would it be for a player to stay hidden in space or on a planet if they don't want to be found?

It's likely, they don't want a button where you press it and boom you found them. Long range scanning will be more analog in nature. You'll have passive scanning where you're collecting radiation over time, then long range scanning you'll be able to view three different spectrums such as Infrared, where it can see through gas and clouds. There will be the visible spectrum of course, but that has its drawbacks. Then there's the X-ray spectrum that can pickup EM signatures which would be great for figuring out where a ship is, but unable to determine what it is.