Hi there. In order to include images along with posts, they need to be hosted by a third party and a link to them embedded or provided, they cannot be included as image files as this site does not have the capacity to host them. There might also be a block (on and off) on new accounts' ability to post or embed links as the site keeps getting attacked by spambots and other evil forces.
The SP options you seek such as Immigration Gauge and many others will not show if SP's progression is not activated because they wouldn't be effective. NRaas > SP > General Options > Enable Progression > True. There is no Emigration Gauge, there are other options that govern different kinds of emigration. They are all off by default and the Immigration Gauge is 0 by default (so no SP immigration). But if SP's progression is not activated, then it is not in control of any of these things. You would then have EA's built-in story progression by way of the Game Options in control, that of another mod if relevant (such as AwesomeMod), or none at all. Only one form of story progression can be active and in control at a time.
1 - Here is our FAQ on how SP works generally.
2 - Yes. Like so many other things, they won't be very effective if SP's progression is not running but they do gate certain things by default.
3 - Not exactly, no. SP consists of many Managers running simultaneously all at different speeds. We can adjust the speeds of each Manager, those controls are located under each major category within the mod's options (higher numbers are slower, because they indicate more sim minutes between each cycle's run) or we can impact the speed of many of them overall with SP > General Options > Adjust Speed. But we cannot be more precise as to what happens exactly when as we can with other mods that have specific time of day triggers.
4 - NRaas > SP > Household (or Sim, Caste, Town) Options > Household: Allow Move Solo and (same menu) Household: Allow Move As Family. Breakups are covered by Romance: Allow Breakup > T/F but note that only covers what SP is allowed to do with sims' relationships. If a relationship degrades beyond a certain point, sometimes the game itself will dissolve it with no warning. Sim and Household Options are on sims and household lots and lot tags, Caste and Town Options are on City Hall and in-game computers.