Couple of questions ?

don't worry about the size... of course you want your map to be downloaded fast but 15mb ain't no big deal at all. actually, hoodoo is 40mb so...

you can edit your skybox by using the enable/disable outputs on the stuff in it.
for your dam, I hope it's not a props, because you can't resize props :\ unless you decompile/edit/recompile which is a pain in the ass if your not familiar with this stuff.

Lightmaps are what add the bulk of size to your map. You control this via the texture/face tool. There is a field that says "Lightmap Scale". The bigger the number, the less "detailed" your lightmaps are and thus, the smaller they are. The default, I think is 16. You can change this default in hammer options so all your new brushes have a higher value (This will not effect existing brushes, you will have to use the face tool). I have it set to 32, which is good for bright outdoor environments with very diffuse shadows and keeps the file size sane. However, all the pros will tell you to fine tune the scales according to your intended light effects and shadows.

As for the skybox / dam, you cannot change the sky texture, but you can use a 3D skybox and design the map so that it parallaxes closer to a dam model/brushes each round.

For the first question make sure you don't have loads of lighting, large areas or unnecessarily tiny lightmap scales. I don't know really, that's all I can think of.

As for your 3D skybox, the magic thing about 3D skyboxes is that if you run 256 units north in the normal one, you will run 16 units north in the skybox.

Don't make your skybox now, however; not until you've worked out where everything is in your main map first (of course you might have already). When you've got it worked out, put a sky_camera where the origin is, copy the most BASIC geometry in your map, scale it to a sixteenth of the size (ctrl+M, scale, 0.0625). Then surround it in the skybox texture, and at this stage i think you should make all of the scaled geometry the texture tool_skip so that you can see where it is in Hammer but is ignored by the compiler. Sorry if you didn't need this mini tutorial though

I think that if you make your skybox dam a dynamic prop and kill it when round 3 begins then you'll have it down, and have round 3 seperate from the other maps.

edit: woooow i suck at typing quickly