What kinds of lightsabers (and fighting methods) are available

The color of your lightsaber is dependent on your color crystal, and you should be able to get any color you desire, no matter if you're Sith or Jedi (or Dark or Light, the below is no longer correct).

Your Light/Dark side affiliation will affect your options though:

• Red (Forbidden to Light 1 and above)
• Blue (Forbidden to Dark 1 and above)
• Green (Forbidden to Dark 1 and above)

See this question for more information on lightsaber colors: What colors of lightsaber crystals are there (and where can I get them)?

Augment schematics are gained from Slicing, and Armormech, Armstech, and Synthweaving can each craft some of them. They can't be bought from vendors, but you should find plenty of them on the GTN.

As to what they are? Well, as you've noticed, they're an item modification slot. They're automatically added when a companion 'crits' on their gear crafting task. You can also buy an Augment Kit (crafted by the above professions) and pay to augment your gear at an Item Modification Station.