4. How do I hide stone on the ground? I heard there is a way, but I can't find the option, and I'd rather not bother clearing it out of the way.
Hit 'd-c-h', select the things to be hidden, then hit enter. You can also use 'k' to examine the item and 'h' to hide it, but that takes a while. If your stock screen is fully updated, you can hide stone through it as well, but it'll also hide any buildings made out of that material.
5. Is there a way to get rid of a channel? So I drained a murky pool to irrigate my farms. Although instead of putting a small hallway up next to the edge of the pool so I could put a door at the end, I just put in a channel between the single wall. I can't seem to remove it, or dig it... or anything. It just says it is a slope downward.
You can designate the slope to be removed by hitting d-z, but that'll leave your dwarf trapped down there unless there's a staircase or another way back up. The easiest thing to do is simply floor over it or cover it with a grate or hatch if you still want to leave the space open.
6. Another: Correct me if I'm wrong, but there's no real way to put a trade caravan zone both inside your fortress, and behind doors right? Since they need three spaces wide, If I want them inside, I have to leave a 3-wide tunnel open until at least the spot where they set up.
There's no way to put three doors in a single line right now anyway so, no. You could use, as previously suggested, a series of floodgates connected to a lever or for metal bars if you want a portcullis effect. Drawbridges are also a good option so long as you remember to set them so it blocks the entrance when raised. .