Too many questions.
First, I think applied research is a bad idea. I think all of the level II and level III facilities are better researched much later in the game. The very slight increase in production just isn't worth it.
Second, stellar manipulation absolutely rules the universe in games against the AI.
I would imagine you can use it with great success in games against humans as well.
Cloaking can be detected with scanners.
It is much faster to convert domed colonies to undomed colonies by transplanting conquered races that breathe that atmosphere.
I've already forgotten your other questions.
I attached an Excel spreadsheet created by WhiteHojo (with some sorting code by TaterBill). This file lists the tech prerequisites for all the techs in the game. The second file lists the costs for all the techs. Sorry it isn't alphabetized or anything. You should be able to use the two to figure out what to research next. I'm a HUGE fan of fighters because they don't require maintenance but can be used with great effect against your enemies.