What do Abundant Luxuries actually do

AFAIK only Ion Torpedoes make use of the production bonus. Maybe in the future (or in some expansion or DLC) they add further modules, but anyhow Ion Torpedoes are really good in the early game to establish a significant firepower difference. Later on (early to mid game), as your production capabilities get better, the production bonus gets less and less significant compared to the loss of firepower you get from using them.

There are three main ways to increase approval:

1. Technologies that reduce expansion disapproval, in the Exploration/Expansion tree at the bottom. Each tech gives you -22% to the expansion disapproval. (Applied Casimir Effect gives you the Colonization Program, Applied Atmospherics gives you Orbital Counseling, etc.) These techs have a green star in the upper-right corner, which is no help at all because almost all of the Exploration/Expansion techs have that green star. You can't just search for "expansion disapproval" in the tech search box, either. The only hint I can give you is that most of these sorts of techs have an icon that includes a guy in a Buddha-like pose, except the first one.

2. Technologies that increase approval in a system, in the Diplomacy/Trading tree on the left. These techs' icons are pink in the upper-right corner, and are a system improvement that gives a flat bonus to approval (and possibly other effects on FIDS) once built. The easiest-to-get examples: Botanical Scanning gives you Infinite Supermarkets for +25 approval, and Optimized Logistics gives you Colonial Rights for +30 approval (and some FIDS bonuses if they're ecstatic, around ~85% approval).

3. Lower taxes; it's a slider in the Empire tab. Keep in mind that, aside from Dust generation and changing your Approval, some races get bonuses for high taxes (Humans get bonuses to both Dust and Industry as taxes go up), others get bonuses for low taxes (the Sophonts gain more research as taxes go down), and others don't care.

Low-approval penalties can hit you twice: once for low system approval, and again for low empire approval. Do not allow your entire empire to become unhappy with you; it's just ugly.

There are a few smaller things that change approval, but aren't universally useful:

1. The less Earth-like the planet is, the more your colonists hate living there. Class V planets (gas giants, asteroids) hit you with -20 to approval; even Class II planets (like Tundra) give you -5.

2. Heroes who are Administrators can grant approval bonuses, but you only have a few heroes.

3. Some planetary anomalies will change approval, up or down. The approval penalties can go away by researching the anomaly-reduction technologies, Adaptive Colonies and Soil Revivification. Of course, you can't add anomalies to a planet, you're just stuck with whatever's there already.

4. Two Endless Temples will increase approval in a system: the Temple of the Aura of Glory gives +40 approval to the system, and the Temple of Applied Psychohistorics gives +10 approval per planet in that system. You won't even know if you have a Temple until you do a Moon Survey (unlocked by Adaptive Colonies), and even then it will probably be a different Temple.

These are the only things that will give you approval. You will eventually need those techs. Higher population won't help - you'll lose some approval for overpopulation as your system fills up. From what I've researched on the 'net, expansion disapproval goes up as you add more systems, so settling a small number of systems with many planets might help.

Note: You only get the expansion disapproval once the system stops being an outpost, a few dozen turns after it's settled. Use that grace period to research some of those useful techs before your approval nosedives.