1: Does the angle of the tiles on the floor (they aren't finished at all) look odd when lined up with the furnace/wall.
I don't think your floor tiles look odd when they are lined up with the furnace or the wall, however, they do look odd because the left side is much more angled than the right side.
2: Does the furnace to wall angle seem a bit awkward? Should I angle either one away? I wasn't really going for a smooth quadrangle room, but are the odd angles off putting enough to be bothersome? I'm thinking about turning the furnace more downward or laterally to match the wall or feel more apart from the wall. ~It might be easier to angle the wall away though, not that easy was my goal.~
You should definitely pull the furnace off of the wall. It's a decent position, right behind him, but there isn't really anything to indicate that it is closer than wall, which it should be. I'm not sure how to explain this exactly, maybe all it needs is shading on the wall, but it should be a separate entity, rather than like a part of the wall.
3: Finally any advice on color palette shifts for the wall and/or advice on how to do the stone tiles on the floor. I was aiming for a sort of diagonal layout of offset square tiles to challenge myself. [Maybe bit off more than I was ready to chew there. ]
I think the diagonal offset could work out fine, but you might try using a color closer to the stone that the anvil is sitting on, rather than the blue thing you've got going on there. I think the bricks on the forge could stand to be a bit darker/redder, but I'm not exactly certain what effect you're going for there.
4: Does the off center placement of the character force more attention on the furnace layout? Should I move him back to the center by widening the shot or cutting off the edge of the furnace?
Are you familiar with the rule of thirds? I don't think that the off-center hurts necessarily, but you could definitely widen the whole shot if you wanted to create a larger scene. I wouldn't cut off more of the furnace, but maybe if you widened it to show the sides of it as well, possibly shrinking the whole thing by a bit it could help.
Another thing I just noticed, it looks to me like the forge is slanting downwards. The line on the bottom of the opening should be parallel to the floor line, but it looks like they get narrower as the go to the left. Maybe I'm just seeing things, but it also feels like the bricks on the bottom half which should be farther away (on the right) are bigger than the ones that should be closer (on the left).
These are just my initial thoughts as a viewer, I'm certainly no art critic; I just wanted to give you a different perspective, since you've probably been staring at for awhile.