Hi,
Yeah the hotspots are community goals and powerplay faction headquarters (Lembava/Sol/Achenar etc). The other places you'll see real players are events or organised things like expeditions
A few hundred are currently flying around exploring in small ships:
https://forums.frontier.co.uk/showthread.php/279327-Small-Worlds-Expedition
The rest are probably in private groups and/or solo mode. The one to join at the moment is Mobius (or the secondary Mobius group since the first got too big), thats PvE only, no combat vs players allowed except specific areas. As a result there's a lot more people just randomly flying around doing stuff and they tend to be more friendly.
The other potential reason your game may seem devoid of player is networking. If your router/firewall/settings are blocking peer to peer as my student router used to do then most players won't get networked with you.
As for Sol yes you need Horizons to land on planets (currently only atmosphere less worlds/planets but more are due in future seasons of DLC).
The Sol permit and powerplay are different things, I'd unaligned because you get attacked a lot more if doing powerplay.
The run-down:
There are 3 superpowers -> Federation, Empire and Alliance
Fed and Emp have permit systems and rankings (see right hand info panel). Information on permits here:
http://elite-dangerous.wikia.com/wiki/Federation
To increase Fed rank you need to find Fed minor factions and do missions (or just trade/bounty hunt or hand in exploration data to Fed factions). Ensure the missions you do are for the Fed factions and have the logo next to the mission giver though as even though they control the station not all missions will be for them. As you do good stuff the info panel on the right of your ship will show your status move through cordial to friendly to allied with the federation as a whole as well as the minor faction, once the right hand "Rank" bar reaches 100% there will be missions around that say things like Federal Navy contract or similar that allow you to rank-up. 4 ranks and the Sol permit should be offered.
Ok now onto powerplay:
Powerplay are influential characters that seek to control systems, some are aligned to superpowers like Hudson, some are independent. They have their own ranking system that degrades weekly, you get cash and access to unique modules/weapons by pledging and doing activities for them.
Finally minor factions:
As mentioned in the first section these are found in all systems and control stations/outposts. They go into war/civil war/boom/lockdown/famine etc and seek to push other minor factions out of the system they are in at the same time as expanding. Doing missions for them and trading/exploring/bountyhunting etc for them helps their influence.
When increasing reputation with minor factions be aware when they reach allied they no longer give as much to the superpower reputation so the best way is to get a Federation minor faction to allied then move along to the next federation minor faction.
Hope this helps
