Really glad to hear you're having fun with the game, welcome aboard!
The visuals are actually all there, and not at all hidden or hard to see. When engines are wrecked, they stop spinning, or are also smoking, though I'm not 100% on that. When a component is on fire, you can see the fire and smoke. You can also see when it's been chemical sprayed. When a ship has taken significant hull damage (about half) it's model changes to one that looks like it has sustained a massive amount of damage. For example, the pyramidion's sail structure is bent and broken, whilst the rest of the ship doesn't look like it can hold up to much more. Also, the game actually tells you when an enemy's system breaks, up in the top left corner, so keep an eye on that to keep track of how a ship is doing. It is a very good indicator.
As for damage types and what is effective, or what isn't, the game isn't going to spoon feed you, but the information is in there. Go into the ship on the top right when you're in the main lobby, then look through the weapons and look at how much damage they do of a certain type. For example, a gatling gun will do more piercing and shatter damage than explosive, which makes it ideal for shredding the armor of a ship, whilst a gun that deals explosive damage is good for when you are directly impacting upon the hull. The two working in tandem together is very effective.
The information is also online, this page might be a bit outdated, but for the general idea of what damage type is effective against what, it should do the trick:
http://gunsoficarus.com/gameplay/weapons/ . You can also compare the damage statistics in game with that web page. For instance, using it, you'll be able to tell that piercing damage does significantly more damage to a ship's armor than the ships hull.
But also, access the community! We are here to help, if you have any questions about what ships/damage/guns are good for different situations, ask away, players have also written guides on pretty much exactly what you are asking for. But in game, it really comes down to skill, knowledge, communication and awareness to defeat ships, not pop up icons.