I think it's a good-looking house, with good proportions. I wouldn't call it "chopped up" looking at all. The mushroom-colored siding and white trim don't do anything for each other. I'd paint the siding (first and second floors both) something like the brick color you're testing in the photo of the front door, but with a bit more orange, and a few shades lighter than the brickwork. Paint the garage door the same color. That should give the house more unity than it currently has, de-emphasize the garage, and solve the "chopped up" issue. Consider painting the lower part of the downspout the brick color as well. I wouldn't use that color for the front doors, though, since you think the doors aren't noticeable enough. White or black would work, as you're already using them for accent colors (and both colors appear in the used brick). Or keep the doors blue. Wait to decide about shutters for the large window until after you've painted the siding. If it bothers you, install shutters; if not, save your money. [Another factor in this decision is the landscaping on either side of the window; will there be shrubs to cover the shutter area? and do you know what the hollies are? Since you're removed most of the shrubs, an updated photo would help.] While shutters are optional, I think a window box under the large window is a definite 'No.' The window is too low. Plant 2-3 evergreens in front of the window instead, and grow flowers in front of them in the warm season. I don't think changing the columns would draw more attention to the front doors, since the columns are in four different locations across more than half of the building. What will help is keeping shrubbery from concealing the area around the entrance. If whatever climbs the trellis will hide the front doors, then move the trellis elsewhere. I wouldn't put anything taller than a foot or a foot and a half in the area in front of the doors. If you want more color in that area, consider adding a narrow bed on the other side of the walkway for some flowering annuals or perennials. How narrow is the narrow bed? Does the porch run the whole distance to the driveway? Am I seeing a walkway in front of the narrow bed, or is that snow? Can you tell us what zone you're in? It will help with the shrub and tree recommendations. If you don't know your zone, you can use your zip code to find out: http://www.garden.org/zipzone/index.php

Chinese pistache is a great shade tree that will tolerate lawn watering. Chitalpa would be a second choice.

The close up makes it certain that it's neither sumac or tree of heaven. Black walnut is a good possibility. In any case, it seems way too close to the house. Personally, I would remove it. You may find it is going to be destructive and terribly, terribly messy.

Pbbb. What do the local weather readers/guessers know about pollen types/sources? Evidently, not much, as you've demonstrated. They're preying on the ignorance of the majority of their viewing audience. I assign no credence to their proclamations. lol