Open the rules.txt and go to the units section where you put it the new unit. At the end of the line (with things like movement, attack, defense etc.) there are a bunch of 1's and 0's, that's the bit you'll be needing.
At the start of the units section it's explained for each of those 0's and 1's what they do.
Here's an example:
Cruise Msl., nil, 1, 12.,1, 18a,0d, 1h,3f, 6,0, 0, Roc, 001000000000000
The Cruise Missile doesn't get obsolete (nil), is an air unit (1), has a movement rate of 12, can stay in the air for 1 turn, has an attack value of 18, defense of 0, 1 hitpoint, 3 firepower, costs 60 shields (6), can't carry any other units (0), the AI uses it to attack (0) and you need Rocketry to build it (Roc)... But this is the part you already knew.
Each 1 in the sequence 001000000000000 assigns a certain property to the unit. Here's what the rules.txt says:
000000000000001 = Two space visibility
000000000000010 = Ignore zones of control
000000000000100 = Can make amphibious assaults
000000000001000 = Submarine advantages/disadvantages
000000000010000 = Can attack air units (fighter)
000000000100000 = Ship must stay near land (trireme)
000000001000000 = Negates city walls (howitzer)
000000010000000 = Can carry air units (carrier)
000000100000000 = Can make paradrops
000001000000000 = Alpine (treats all squares as road)
000010000000000 = x2 on defense versus horse (pikemen)
000100000000000 = Free support for fundamentalism (fanatics)
001000000000000 = Destroyed after attacking (missiles)
010000000000000 = x2 on defense versus air (AEGIS)
100000000000000 = Unit can spot submarines
As you can see, for the cruise missile, the 3rd digit is a 1, which means it's destroyed after attacking.
Limiting the availability of a unit to one government, however, is not possible, with only one exception: The unit in the Fanatics slot in the units.gif can only be built by Fundamentalists. Any other unit can be built by anyone.
You can let any unit have free support under Fundamentalism with the 4th digit in that sequence of 1's and 0's, though.