[MegaTrain]

1) Let's see if I can remember them all:
Escort - 150kt
Frigate - 200kt
Destroyer - 300kt
Light Cruiser - 400kt (can support Large mount weapons)
Cruiser - 500kt
Battle Cruiser - 600kt
Battleship - 800kt (can support Huge mount weapons)
Dreadnought - 1000kt
Base Ship - 1500kt (can support Massive mount weapons)

2) Yep, its called Stellar Manipulation. I think you need Physics level 2 or 3 to be able to research it. I think you get warp opening/closing at levels 3 and 4, and sun destroying weapons at level 5 or 6.

3) Regarding the Organic/Temporal/Crystalline weapons: you can only research them if you've chosen their research tree as a racial characteristic of your empire at the beginning of the game.

With that said, they are some of the most powerful and efficient weapons in the game. Take Organic weapons, for example. With a single research area (a fairly expensive one, I'll grant you), you can discover specialized missles, long-range weapons, and short range weapons, some of which have nice advantages, like a faster reload time for the missles. Another advantage is that your ships become more resource-balanced instead of mineral-heavy, and can be built quicker.
I don't know much about the Crystalline weapons, but I know that some of the advanced Temporal weapons can be pretty deadly.

[Edited Baseship size and spelling errors]

[ 08 December 2001: Message edited by: MegaTrain ]