How much capital ship piloting and influencing the game universe can you do? Can you create your own faction? Fight other factions, conquer territory?
Depends on when/if you get a capital ship, then there's piloting of it. It's a sandbox, and while there is a campaign, they don't give you a capital ship (although I've only played X3: AP and only the main campaign for that).
You are your own faction, sort of. You buy your own ships, you set the AI orders for ships you're not actively piloting, you can build your own factories, you can build your own shipyards, etc.
You can fight whoever you want to, and there are several factions that start hostile depending on your start (There are some preset starts you can choose from. There's also a 'custom start' I believe). You can declare war on an entire race if you want. There are war mechanics in X3: AP, but I believe it's only between the Argon and the Terrans and it's not well-managed (fixed by mods). X3: TC I believe has way more faction war stuff, but AP is the improved version, so *shrug*
Conquering territory, other than the war mechanics, involves you either out-competing all of the economic factories in an area and you just dominate the trade completely so you pretty much own the sector, or you just blow up everything in a sector. It's not easy though, it's definitely an all-out war between an entire faction and you if you want to go hostile.