How does one get more wealth?
The primary source of wealth comes from a tax on the number of citizens you have in total, so your best option is to get as many populated colonies up and running as you can and help them grow.
The second source of wealth is civilian shipping. Colony ships will transport colonists from high pop to low pop colonies. Freighters will transport Infrastructure and, after the colony has grown large enough ship trade goods. Luxury liners will ship small amounts of population between any colony, including established ones. The wealth per run for each of these is based on the distance travelled, so having colonies in other systems linked by jumpgates can result in higher profits. Well developed civilian shipping can result in greater wealth income than from your population taxation.
The third source of wealth are financial centres, that can be built on any colony with a population and will use some of your workforce to provide a small amount of wealth. It takes a large number of these to make a significant impact, so it is usually only worthwhile on a world that is not otherwise using it's population to support mining/construction/research/shipbuilding.
The fourth source of wealth are the CMC's, Civilian Mining Concerns, that will pop up on asteroids/comets that have been found to have minerals but have not had a colony created on them. They can be set to sell the minerals they mine to the civilian market resulting in wealth for you or you can spend wealth to gain those minerals for yourself.
Also, is it possible to use salvaged ship components in fighter production? I built my first class of fighter, realized I needed to upgrade some stuff, but couldn't find a "refit fighter" option or anything like that (is there such an option, btw?) so I had to scrap them. The new one used most of the old fighter components that were taken from the old fighters, so logically I should be able to use the salvaged components. Unfortunately, when I went to build the new fighters, they didn't use any of the stockpiled components. Is it just not possible to do so for fighters?
Fighters can't be refitted, I believe this was an intentional decision by Steve. However stockpiled fighter components should be being used when building new fighters as long as the exact component is part of the design. If it is not it is a bug that needs to be reported over on the aurora forum.
When do jumpgates spawn? Is it only when NPCs build it or does it spawn with NPCs, or can they be just remnants of the past?
When each system is generated upon being entered for the first time(whether by you or an NPR), each jump point in the system has a small chance to have an ancient jumpgate built. Other than that jumpgates are only present if they have been built by the player or an NPR.