1. Ship Upgrades (offensive). Thoughts on this? Worth its salt? (e.g. the Illumi Beam Upgrades (to30%))
Regarding advent and illuminators, I would say that early-mid game shield, hull, and guardian upgrades are much more important. The first two beam upgrades are expensive, and only increase the average beam damage (if you look in game) one point per upgrade, whereas the first few shield and hull upgrades improve each by about a hundred points, and are relatively inexpensive (until you hit around level 4).
I have lost battles where I had almost 10 more illums then the other guy, simply because he had more hull upgrades and a higher level of malice.
2. Worth paying to upgrade your caps?
It depends on the opponent, and again I am speaking for advent. If you are playing someone where you will have a fight on your hands relatively early, and a stiff one at that, then it probably would not be a bad idea to pay for the first couple levels to get to level 2 malice fast. Even the first level upgrade may be worth paying for in general as it is fairly cheap (about 656 I believe).
3. Many people recommend sending out LFs at the beginnging with cap ship... Why when the cap ship can do the job by itself (colony) and you can save the much needed creds you spent on the LFs on boosting your feeble economy?
I almost never send light frigs out with my cap ship. The cap ship alone is fine for dropping roids and 1-1-1-1 planets, and any planets with significant militia I usually just wait until i have long range frigs. Early game that cred is better spent getting to long range frigs faster...