Firstly: Yayyy Star Control 2!
Secondly: You really have to stop thinking in terms of "classes," I think, because in Allegiance, you will need to switch ships often, depending on what your team needs most. Also because not all types of ships will be available depending on what technology your team has. Also, because all ships need to be stealthy sometimes; I mean, I get that you're talking about stealth fighters now, but being stealthy is important with many different ships, depending on the situation.
Anywho, while you definitely *could* go around killing EWS probes in a stealth fighter, you should really do that in a scout. The scout's superior sensor range will make it easier to find enemy probes, and you can have a cargo full of probes of your own to deploy, expanding your team's situational awareness even as you reduce your enemy's. Also, scouts will usually attract less attention than a stealth fighter, since when someone sees a SF on the mini-map, they'll usually assume it's hunting for miners. Also, you really don't need stealth to hunt for enemy probes. Teams typically check whether they have enough probes around, and re-deploy them as needed, rather than wasting time hunting down individual ships that are trying to kill probes. Even if they see a specific ship taking out probes in a given sector, the reaction is usually to assume the enemy is about to attack from that sector, and re-deploy probes there, rather than to go hunting down that one ship (unless there's an opportunity to do so easily. I mean, no-one would chase you across three sectors just for killing probes in a scout.)
The main purpose of stealth fighters is to kill enemy miners by hunting for them while remaining stealthy, then launching a few missiles at the miner while beginning to approach it, and then finishing it off with Util cannons. Of course that's not ALL SFs can do, with good technology and an early warning they can be good defenders too... but that's their primary function.
Aside from probes, scouts are most useful in providing the enemy with situational awareness, obviously, but, yes, any ship will let the enemy see what's around it. Scouts just have the most sensor range. So yes, if an enemy miner sees you, the enemy team will know you're there. All information from all ships, from miners to scouts (and bases too), goes onto the team's mini-map (
always have the mini-map on, press F7 if it isn't.) But scouts are the ships that are meant to go around spying on enemy movements, so if you're trying to be stealthy they're what you need to worry about most.
When you first enter a sector, no, you will not instantly know all the resources there. You have to "discover" the relevant asteroids. In practice, scouts' high sensor range and the relatively high signature of asteroids means that you'll discover most of a sector's resources very quickly as you start to fly through it, but you likely won't see ALL the helium rocks in it right away. If you're in a scout, you'll usually see the tech rock (carbon/uranium/silicon) right away though. Ships with lower sensor range might enter a sector and see nothing at all, however, and all the resources will remain invisible to the team. So, as you hopefully know already, only try to scout in... scouts.
About stealth: Any ship can be made more stealthy by stowing shields and missiles in cargo. Have your ship's manifest open (press F4) and if you have free slots in cargo, press Ctrl-7 to unmount shields, and Ctrl-5 to unmount missiles (if you don't have room, you can press Ctrl-S to eject cargo and make space... just don't eject something you'll need later by accident!) This lowers your signature. Once you've been detected, or when you're going on the attack and know that you're about to be detected anyway, you can re-equip them by pressing those keys again. Always do this in stealth fighters, or they won't be very stealthy.
Stealth is important for other ships. Bombers and Heavy Troop Transports will try to remain undetected as long as possible when approaching an enemy sector. Heavy Troop Transports particularly will try to hide in enemy sectors while remaining undetected, moving to the best angle for the attack run. If you're going to be nanning the HTT in a scout, make sure to drop your shields and don't have any missiles loaded, because if your scout is spotted, someone might follow it to the HTT. You can raise them again once you've been spotted, after the attack run is already well under way.