You understood the game pretty well despite our poor attempt at explaining it in-game. I'll try to explain all the inner mechanics of the game along with the numbers. Long post incoming, but I'll label the sections so you can navigate it better hopefully.
Timing
Yes, the combat rounds have a 15 second timer. The player has to make all their decisions within that time, that's the challenge of the combat game. (There is a crew member perk that adds 3 seconds to the combat timer to make it easier). Once you get the flow of the combat you can get good enough that you won't even need the full time. Then you can press the big red Fire button on top of the sliders to instantly drop the timer to 0 and start that round.
Meters & Weapons
The 3 meters are guns, shields & thrusters. Guns are how much damage you do, shields are how much damage you block, and thrusters increase your chance to dodge & crit. The value of the gun and shield meters are the values you will hit for and block respectively. The value of the thruster sets your dodge chance to 50% of the value and your crit chance to 25% of the value. Crits deal 2.5x damage. The total values for all the meters add up to your ship's reactor value. By default your reactor starts at a 100 so you get to distribute 100 points between the 3 meters. There are research options and crew perks that increase this. And yes, you use the sliders (left side, front console) to set the meters. The gun and shield sliders have 3 buttons each above them to set their respective element.
Nukes deal 100 damage instantly and stop you taking any damage for that round, but also injure all crew members so it's a risk-reward tradeoff. The nuke also takes about 5 seconds to arm so you have to make the decision to use it fairly quickly.
The element system
The element system is rock-paper-scissors. The 3 elements are called: Ballistics, Laser & Plasma. We made the "weak against" and "resistant to" based off pokemon's typing matchup system. If you match your shield to properly block the enemy gun, you're resistant and take very little damage. If you get completely the wrong type (the type that's weak against it, think a fire type in pokemon fighting a water type), then you take high damage. If you use the same element as them then you're partly effective and take medium damage. The element strength matchup goes likes this:
Ballistics > Laser > Plasma > Ballistics
This applies for both when you're choosing your gun type against the enemy's shield, and also when you're choosing your shield type against the enemy gun.
Injuries
Your crew members also have a chance to get injured, proportional to how much damage you take in that fight. So if you fight recklessly and don't block much, your crew will have a much higher chance of getting injured. A dead crew member doesn't contribute their perks anymore so that's a big loss. If all 4 crew members die, that ends the run.
Round example
Enemy sets: 50 guns (plasma), 30 shields (ballistics), 20 thrusters
I'll set my shield to about 40 so I can block most of the damage. I want it to be laser, since laser is strong against the enemy's plasma gun. (If I chose plasma, the same element as the attack, I would only block half of the damage, or 20. If I chose ballistics, which is weak to plasma, I would block 0 damage!)
Since I used up 40 on shields, I have 60 left for guns and thrusters. I'll set thrusters to 20. This gives me a 10% chance to dodge and a 5% chance to crit.
Now I have 40 left and I'll use that for guns. I'll set the element to plasma, since my plasma guns will beat the enemy's ballistic shields. Because I got the typing right, the enemy will block 0 damage so I get the full 40 damage in. If i crit then that's 2.5 x 40 = 100 damage.
My final setup: 40 guns (plasma), 40 shields (laser), 20 thrusters
Another round example (w/ Nuke)
Enemy sets: 80 guns, 10 shields, 40 thrusters (higher level enemy with 130 total reactor, 90hp left)
Lets assume my ship only has 140 hp left. The enemy has a high chance (10%) to crit here and kill me. I can either set high thrusters myself and try to dodge, or set my shields very high (~80) with the right element and try to tank the hit, or I can use a Nuke.
I decide on the Nuke. I take no damage for the round so I save my ship, and the nuke does 100 damage and destroys the enemy. The drawback was that all my crew members took injury damage and I'll now have to use biomass to heal them up.
Conclusion
Hope that explained the inner working of the combat system. It's a lot to throw the player into without properly guiding them through the mechanics. We tried to explain the basic system in the in-game help (H key brings up help any time in-game and explains whatever activity you're currently doing) but of course that's not really an ideal way to do it. The post-jam version of the game will hopefully do a much much better job of guiding the player through the mechanics so they can pick it up intuitively and then naturally get better at it over time.
Thanks a lot for your interest in the game and making the effort to understand it. We put a lot of thought into making the mechanics fun and strategic and really appreciate your effort!