That's why a lot of people quit around this time lol; the nature of the game fundamentally changes. Battles become fewer (at some point you're only manually fighting epic major ones and auto-ing the rest) while managing numbers becomes the heart of what you do. It basically becomes more of a proper strategy game like Nobunaga's Ambition or something and less of a tactics-focused game.
1: Taxes, battle loot, and workshops. Caravans are a no-go because they're mostly likely going to get wrecked whenever there's a war going on. Taxes vary wildly dependng on the quality of fiefs, but a rule of thumb is that they can support ~2-300 soldiers before going into the red when lower quality (like, less than 3,000 Prosperity) and up to, I dunno, a thousand when very high quality (10,000 Prosperity). Workshops usually provide around 100 denars per day, and my best luck is just buying the local workshops without changing them since changing them usually results in either oversaturation of the market or resources being too scarce and thus a net negative in another way. Not enough for a large army but every bit helps. Battle loot from large enemies (like hundreds of enemies defeat) can net anywhere from tens of thousands to hundreds of thousands of denars (and more if the enemy's mostly high tier troops) so boldly hunting for wayward enemies is a very profitable business in exchange for the inherent risk of losing troops and even acquired loot if you're defeated before liquidating it in time.
2: By ignoring it. As a vassal, you don't need much Influence so just bottle it up as you fight battles and passively accrue it. Really, as a vassal, you'll never be able to spend more than 200 for a "quadruple vote" per issue anyway, and gathering a large Army costs around a couple hundred as well, so it's really more of an issue for monarchs than vassals.
3: There's a mathematical formula for it, and it goes something like this (in order of priority): Homeless + Proximity + Clan Military Strength + Conqueror + Ruler + Player divided by Total Clan Prosperity equals your numeric value in being one of the tree voting options.
In other words, once you have a fief, your best shot is to take fiefs adjacent to it. If you don't have a fief, you're effectively guaranteed one. To prevent clans from having TOO much territory, total clan prosperity makes it so proximity only takes you/others so far but... that can be a while. Furthermore, being both conqueror and human gives you a marked advantage as well.
Trying to conquer rebel cities is no easy feat; you'd be trading the slow grind to power for a very high risk one that, while potentially much faster, could just result in you being stomped very quickly--unless you never formally establish a country, since I hear being an independent clan is basically an exploit since nobody will ever declare war on you, but if you don't like the idea of exploiting the game I can't recommend it, so the "hardcore way" would be to fight everybody around you and try not to go broke or get dead (for real dead) in the process.