OK, now on to SM
Level 1 just gets you the ability to make and destruy storms, BFD.
Level 2 gets you the ability to destroy Medium or smaller planets, and also to make Medium or smaller planets from asteroids. Look at the size and characteristics of the asteroid cluster, those will be the size and characteristics of the planet you make.
Level 3 Stellar Manipulation finally gets you the ability to open and close warp-points, along with the ability to make and destroy planets of sizes up to Large.
(The above descriptions contain certain minor simplifications and omissions.)
Cloaking. You can research Cloaking after you have Physics Level 3. You can counter Cloaking with several different types of Sensors. Military Science L2 allows you to research Advanced Military Science. Levels 1 through 3 of that (AMS) let you build various training facilities. Levels 4 through 6 of AMS allow you to use Hyper-Optic Scanners. There are also Gravitic Scanners, which require Gravitic Tech. There are a third kind of scanners, type I can't think of right now, that are always available to all races. In addition, some of the specialty race characteristics allow specialty scanner types. I think Psychic races can build Psychic scanners, and Temporal races can build Temporal scanners.
For a really very good explanation of Cloaking and Scanning, look at the manual. The first section of the index on the left, headed Game Details, run down the alphabetically-listed subjects until you come to "Sight". Click on that and read carefully
Oh yeah, that third normal kind. Scanners, the tech itself, (not to be confused with Sensors, which get you to-hit bonuses in combat. The first few levels just let you peek at an enemy ship's components from a distance. Then the next few levels allow you to use Tachyon Scanners, which are another way to find cloaked ships
Scanners should become available for research as soon as you complete Physics 2
[This message has been edited by Possum (edited 02 March 2001).]