Not really, though they are truly quite rare because the only people that can grant them are High Lords of Terra, and their depiction in TTS is pretty accurate.
There's actually different levels of Warrants of Trade, with different limitations on them and exceptions in place. Obviously the most powerful and far-reaching are the ones issued by the Emperor, then the ones issued by the High Lords. But I think sector Governors can also issue a more limited form of the Warrant of Trade as well. I know for a fact they can grant licenses to Chartist Captains.
...not really, actually. Warrants of Trade are quite very much said to be "FUCK YOU" papers, quite similar to the Inquisitorial Rosettes. Obviously, practically proably people would be more likely to listen to a dude with a paper signed by Big E himself rather than some Primarch (they gave out those too) or High Lord of Terra, but technically all of those are on the same level and there are no limitations except few conditions (visit that-and-that world, colonize, spend majority of time outside Imperial space etc.) but those are specified in the document itself and vary from Warrant to Warrant. There are few ways to lose it (though they all are basically "actively working against the Imperium"), but really, if you have one you're set for life.
Letters of Marque are the ones that you could proably get from Sector Governor - they're usually limited to a said sector or, if they were issued by High Lords of Terra, by some other limitation. Those are also usually not hereditary.
Charters are different because they don't really give you the possibilities of Rogue Trader, those are just papers that allow you to ship shit around with your designated ship and get cash. The Free Charters are nicer because they allow you to do fuck-all (including getting battleships, if you can) as long as you trade, but you still don't have shit on Rogue Traders.
The Warrants of Trade usually don't matter a whole lot anyway, as local authorities and private citizens are prone to bending the rules anyway since oversight is so infrequent. They only really matter for things of sufficient importance or scale that a clandestine civil war is likely to break out anyway.
I assure you that fake Rogue Traders, if somehow discovered (not that they are usually actively pursued, but then barely anyone has balls to do it) would be hunted down like crazy. Impersonating Rogue Trader is literally as bad as impersonating an Inquisitor.
Also, I assure you that without proper papers and shit you're as good as dead in space. Imperial Navy captains are really fucking bent on proving themselves while also not getting died, so if you start to fly around without proper permission and sell stuff/do whatever, you will stumble upon some frigate or even some sector defense forces sooner or later and if you don't prove you're good then GIT REKT SKRUB YOU JUST PROVIDED ME A PROMOTION. Space travel in Wh40k is elitist as fuck.