1: I'm not sure, as I also don't usually mothball ships; if I do, they rarely have cargo on them
2: Personally, I'd stick to maybe 80% research facilities, roughly 12% miners, and 4% each of organics and rads. As a side note, my usual mix if I'm in contact with other empires and need to both research and build up some decent forces is roughly 40% research, 40% minerals and 10% each organics and rads.
3a: Don't know if fighters can be mothballed on their carriers; I suppose its essentially the same question as #1.
3b: Depends on the answer to 3a
4: Defenses: Definitely have decent point defense. About level 4 leaves you essentially invulnerable to missiles as long as you aren't horrendously outnumbered. If you put about 2 PD per ship, you should be in great shape.
You'll also want armor; specifically scattering armor and stealth armor. At their highest levels (3), they each give you a 15% defensive bonus. This brings up another point; research ECM and Combat Sensors to their max.
Offensive: Phased Polaron beams are excellent as Urendi Maleldil mentioned, up until your enemies get phased shield generators. But that will be quite some time in the future, so PPB's should be great for a long time.
5: Urendi Maleldil mentioned the most pertinent points on Stellar Manipulation. Expermentation will reveal the rest
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