Fraid i don't make new factions, i know how to do everything for factions once in the game, but not for brand new ones. All i can suggest are:
They need to be enemies with the ones you offer missions against. Best example, liberty police aren't enemies of the corsairs, so if you put those two in the same system, you will get no missions available at the base.
Make sure that all the initial world and the empathy etc has your faction in it correctly, and set up right.
Have you got them in enouncters in your system? Best way is to make an ambient population, then put them in an encounter for the system - and for thier enemies faction too - so make sure they are available (so they can have missions against them)
The base needs to be set to that faction. Make sure their base belongs too in the mbases.ini is for your new faction.
Next - the code in universe is for the same thign - whom runs the base. You won't have one, so pick one that is closley matching your faction i assume, like if they are similar to bounty hunters - then choose bounty hunters.
Make sure you have a mbases entry, and that it is offering missions! Simple taht one - also, make sure your mbases file isn't corrupted. DL the SDK from EOA players consortium. That way you will get a fixed mbases.ini file (it takes about 2 hours to fix it manually if you do it by hand -i did, trust me, download the pack!).
Next - make a character for your faction in the bar, that is the easiest way to do it, make them an 'offers missions = true and mission_type as destroy.
Now - make sure your system has plenty of vignette zones - a bit like this:
[zone
nickname = zone_A01_destroy_vignette_3
pos = 2943, 0, -17552
shape = SPHERE
size = 10000
mission_type = unlawful, lawful
sort = 99.500000
vignette_type = open
[zone
nickname = zone_A01_destroy_vignette_4
pos = -4861, 0, 30674
shape = SPHERE
size = 10000
sort = 99.500000
mission_type = unlawful, lawful
vignette_type = open
Notice they are unlawful, lawful - so both can use it, and open type. Spread them round - lots of (they can overlap) and then make sure they are covering other encounters zones - like zones around the base or something. This gives you missions.
Do you see your faction flying round? Do you see their names - cos i don't know whatcha done, i cannot help out anymore than that. Sorry i didn't give examples for each part - but i woulda been typing all day
Make sure your object (base) is also set as your faction in rep. How do other supposed 'enemy' factinos respond to yours (do they react to you at all?).
Anyways - good luck, i have also heard about probs with factions in SP - but till i make one (gotta try it soon i suppose) i won't know more.
Chips