Contribute to community goals while playing solo

You get merit points by participating in pretty much anything Powerplay related. Expansion, Fortify, Prep, Undermine, etc.

The easiest and most painless way to do it is by Fortifying (although it is very time consuming). You do this by collecting fortification materials from HQ and delivering them to a control system that you own. Preparation is a similar action, just taking the data to a new uncontrolled system from any controlled system. (1 merit per item)

Expansion for Arissa has you enter the prepared system and enter a conflict zone like area. Other powers have different objective, but it's still the same rewards. The merits aren't much (1 per objective) but a decent amount of time and hanging around allies could get reasonable merits pretty quickly.

Undermining and Opposition is by far the best way to get merits, but it is also the most dangerous. To undermine powers not aligned to your major faction, you must go into their controlled system and kill specific transport ships, either by interdicting them or hanging out in the nav beacon. Undermining and opposing an ally major faction has you pirating these transport ships instead of killing them, try and do this as non-combat as possible, they are allies after all. Be warned, this will be an illegal act and attract bounties on your head as well as the security force coming down on you. (15 merit per kill/loot)

If you attack any ship that is in a power aligned to your major faction, you will lose merits, so always avoid lethal engagements with allies. (-10 merit per ally kill))

You call them "local" factions, but I prefer "minor" factions, since they can have a presence in multiple systems.

Benefits include:

• You get friendly/allied with the major factions by becoming friendly/allied with multiple of the minor factions allied with them. Being friendly/allied with major factions makes you automatically friendly with all of their minor factions, and has other benefits.
• Lower fuel and repair costs at any station they control.
• More/Better missions on the bulletin board. If you look at the bulletin board, you can see that missions require a minimum reputation with the faction posting the mission, and some require "friendly" or "allied".
• In a few cases, it's how you gain a permit to a system. There's a bunch of system permits tied to military rank with the Federation and Empire, but there's also systems controlled by minor factions that you have to get friendly or allied with to get the permit.
• Less attention from their system authority (police) ships. Less likely to be interdicted, slower to get scanned on your way into a station, etc. This makes travel in that system easier, and especially makes smuggling easier.
• It's further from "Unfriendly" and "Hostile". Those have definite disadvantages, and you can get away with more things before you get there if you start at friendly or allied.
• Their ships show up green on your scanner. Depending on what you're doing, this can be helpful. I find bounty hunting in a friendly/allied system easier, since I can skip scanning green ships.
• You get nicer messages from the station when you request docking.

If you rank up from "Friendly" to "Allied", it's basically just more of the same types of things.