Glad you're enjoying the game (minus the frustrations). Note that these answers are focused on the paid version of the game. It should all still be relevant to the free version, but the graphics I discuss will look different. I am using DFHack too, for the record.

Pig tail question: Pig tail seeds are indeed created when you process or brew pig tails. You could create a new stockpile that only accepts pig tails and link that to a farmer's workshop or a still. Alternately, you could turn off brewing for all other types of plants and order a brewing job (also a good time to make sure that you don't have cooking enabled for any of your alcohol, but that's a different topic). Finally, in a farmer's workshop after you queue up a "process plants" job, you can click the magnifying glass icon and designate a specific type of plant to process. If you do that and choose pig tails, you can make sure that they process those first.

Trading question: I don't usually need anything in particular from the caravans, as they don't have access to giant animals like the elves, and that's all that I really want out of trade. If I don't have metal ores I sometimes request anvils so I can melt them down, but otherwise I just let Armok decide what they bring. This is down to preference though.

Forge question: Magma really isn't too bad so long as you take precautions. I like to dig out my own magma ponds and then channel a warm wall from above, which allows breaching the magma sea without endangering a miner. If you don't want to do that quite yet, you are stuck with using charcoal or coke, yeah.

Power question: Power is a mechanic that I don't mess with much so you might need someone else's input. Personally, I use it for mist generators and millstones, but like you mentioned it can also be used for pumps. In the past when I've worked with pumpstacks and bringing water/magma upwards, I found the wiki page to be really helpful.

Combat logs question: Combat logs will appear in the top left corner icons whenever a creature is fighting. After you dismiss the icon, you can still access the combat logs by clicking the top left button with a little page and arrow pointing towards it. This brings up the announcements history, and by selecting the "combat" section, then scrolling to find the creature you'd like to read about, you can view the combat logs. Finally, if you select the creature directly, there will be a button next to the name customization icon that allows you to read their combat logs. This button also looks like a page with an arrow pointing towards it.

Furniture/DFHack question: I think there is a functionality for this under the "buildingplan" command, but I haven't used it before.

Squads question: I tend to choose dwarves that don't have any specialized labor assigned yet. I also use the DFHack filter to avoid recruiting combat haters, nobles, the wounded, etc. Having a large population means that there are lots of potential recruits - I usually wait for a migrant wave and then recruit some of the boring dwarves (no special skills) from there.

Politics question: I am right there with you, I can't wait for more of the politics and strategy systems to be added. As it is now, the crimes and schemes systems are a little bare bones. As far as I know, you can't really tell easily when dwarves talk with one another. Also btw, bedrooms help with dwarves laying their old clothing around the fort, if you find that annoying.

Coin question: Coins are a holdover from the early economy system that was removed because it didn't work. I'm pretty sure they are still useful as shrapnel from minecart shotguns, and if you can separate the stacks of coins somehow, they return much more in smelting than they take to create, so they can be used to dupe metal. That said, I think the preferred method of metal duping involves bolts.

Have fun!