I tried to cast epoxy resin on a pine cone, and used 1kg total (resin + hardener). I used around 3 drops of dye but the object is too dark now (and not see-through). Is there a way to somehow make it more transparent after it has hardened?
From the pictures, it looks like the problem is transparency rather than darkness from too much dye. In fact, the tinting is barely visible, so ignore my comment about trying to fade the dye color.
From the sides, it looks a bit translucent rather than transparent. That could be from the dye causing cloudiness because it isn't compatible with the resin, or the resin surface being a little matte. There are tiny spots scattered around that look clearer, which suggests it's the surface.
The top view looks much more transparent (also suggesting it's a surface issue), although it's very distorted. The top surface is very uneven. That suggests that the resin was disturbed after it started to gel and harden. That very irregular surface would explain the distortion.
A cloud of microscopic air bubbles is another thing that can make the resin look translucent. There are a lot of air bubbles at the top, but they are much larger than that. If those weren't introduced by mixing, they may have been trapped in the pine cone, and didn't all escape before the resin started to harden.
If you repeat this, use much slower setting, less viscous resin. Trickle it slowly outside the pine cone so the resin level rises slowly, allowing the air to escape as the resin flows into the nooks and crannies. This kind of project would really benefit from a vacuum chamber.
So what to do now?
I would start by washing it with alcohol, then soapy water in case what you're seeing is just a film of whatever you may have used as mold release. As a further confirmation that the translucency is due to the surface, look at whether it's more transparent when the outside is wet. If the problem is that the resin is cloudy, there's nothing you can do now. But from the pictures, it doesn't look that way.
If you confirm that it's a surface problem, you can either polish it, as Matt suggested, or coat it, as Elmy suggested. But if the problem is the surface, it is extremely superficial. Before tackling Elmy's suggestion, I would just try to buff it, maybe start with one side to determine if that approach will be sufficient. I wouldn't even use sandpaper. If just buffing with a cloth doesn't do it, try buffing it with a very mild abrasive like toothpaste to polish it, then rinse it and buff again with a dry cloth.
This cast was probably too high for this specific resin and due to the exothermic reaction the resin heated up so much that it boiled. That's why there are gigantic air bubbles in it and the surface looks so distorted. You can see a demonstration of epoxy boiling in this video.
Resin is a complicated material to work with. For perfect results you want to mix very exact amounts of resin and hardener and you want it to set in a controlled way. Once the 2 components are mixed together, they start a chemical reaction that produces heat. At the same time, the reaction is accelerated by heat, which in turn produces even more heat. It gets out of control very fast.
Once the temperature reaches a critical point, the resin starts bubbling and steaming like boiling water and it sets extremely fast (I've had a resin with 24 hours curing time bubble up on me and set in 1 hour once). This steam is very unhealthy and you should put the cast outside and leave it alone there immediately. It's lost anyways... Maybe put an upside-down bucket or anything over it so no animal or other person touches it or breathes in too much steam.
The only way around it is to cast several thinner layers one after the other cured. Resin is a bad heat conductor, so you have to make sure that each layer is thin enough that it cannot even create too much heat. Whether the layers are horizontal or vertical doesn't matter. If you are careful with the amount of dye you cannot even see the separation between the layers. The safety data sheet of your resin should contain the maximum safe layer thickness.
To improve the clarity of your cast you have 2 options: either polish the resin to a mirror finish or coat it with a final coat of resin or clear varnish. Polishing is a lengthy procedure that requires much patience and experience.
A much simpler and quicker fix is to pour a final layer of varnish or epoxy over it. You'll need to sand the existing surface with coarse sandpaper to make it even more rough, or the epoxy will pull away from some areas (which is very visible in the end). You'll need to put the pine cone on a stand where excess epoxy can drip off. And in my experience this works best with an epoxy as viscous as honey (so it doesn't flow off too quickly) or with UV resin you can cure quickly. Have some tool at hand with which to move the epoxy around to cover every spot.
The final step: declare the side with the bubbles as the backside ;)