Open your GalaxyScenarioDef.galaxyScenarioDef file, it contains all the starting templates. Your new race isn't in there, so it starts with nothing, not even the two constructors.

To add it, scroll down to :

playerTypeCount 4
playerType
    designName "Tech"
    entityDefName "PlayerTech"
playerType
    designName "Psi"
    entityDefName "PlayerPsi"
playerType
    designName "Phase"
    entityDefName "PlayerPhase"
playerType
    designName "Pirate"
    entityDefName "PlayerPirate"

You'll need to add yours in there, and increase the playerTypeCount. "designName" is what you use to reference items inside the file, and the entityDefName is the name of the entity file. If you have any new units or non-standard units/buildings you want to start with, you'll have to add them to the "planetItemType" list just above the playerType list. The ItemType list works the same way. It has definitions for a bunch of units and buildings already, but you may need to add some.

Anyway, once you added your race it's time to give it a template. Right below the playerType list are the planet templates:

planetItemsTemplateCount 25
planetItemsTemplate
    templateName "Empty"
    subTemplates 0
    groups 0       
planetItemsTemplate
    templateName "Template:DefaultHomePlanetSetup"
    subTemplates 0
    groups 3
        group
            condition
                type "PlanetOwnerIsRace"
                param "Tech"
            owner "PlanetOwner"
            colonizeChance 1
            items 3
                item "Tech:Module:CapitalShipFactory"
                item "Tech:Frigate:Constructor"
                item "Tech:Frigate:Constructor"

(there's Phase and Psi there too, but they look the same so I didn't paste them). So here's the default home planet setup for the TEC (the paste is from a mod I made so it has the capital factory instead of a frigate factory). As you can see, "Tech" is the designName in the playerType list. All you have to do is add your race to the "groups". So you'll now have 4 groups, and it will look the same besides replacing "Tech" with whatever the designName for your race is, and the items with whatever you want it to start with. The entry will start with "group" to symbolize the start of a new race, just like the TEC template starts right below the group count.

Yep, you can add whatever you want provided it's declared in the planetItemType list Just make sure all your counts are updated, or it will crash horribly!

I actually do not think that's possible. A player needs to have a starting planet or the map won't work (since the victory condition is destroying all colonies). This can't be changed, so no colonies is an instant defeat. Can't use an asteroid field for the same reason, since it can't be colonized. You could use a dead asteroid, I suppose, since it has no population, no mines, and generates no income.

But then someone will just have to destroy it and you lose the map - with no other colonies of yours to attack everyone will go to town on your little rock

You can't set any techs to researched at game start. You always have to start from scratch - unless I'm misunderstanding what you're asking?

That could work. You can give the base the planet shield ability that absorbs 100%, so while the base is standing (or floating ), the asteroid can't be bombarded.

The TEC's planetary shield module?