1. When you craft a character, do you take other existing characters into consideration? I.E. Do you think about how your character can interact with others? Do you think long-term or do you prefer to let it develop based on the dynamics the role-play will, later, establish?
Most of the time, yes, other characters influence, either by intentionally making them similar or not. Playing out their actions and reactions, before using, helps, because I don't want the other author's or my desire for a certain direction to override that person's character. I try for long-term, but it's always like discovering a delightful surprise whenever any of them are in the right position to do this/have that.

2. When creating a character, do you throw random traits together or do you proceed in a logical fashion of: good trait, bad trait, good trait, bad trait, etc. Do you always have to "balance" your traits?
Nope. It can go any way. What matters is a basis for them, where history and character bounce off of each other, until there is an end result.

3. What kind of process or system do you use to go about constructing a character?
If it's not inspired by an appealing sensory basis like a story, thought, music, a picture and so on, then I work off a system based on numbers: 1 (Entirety), 2 (Genders), 3 (Descendents), 10 (Easy to Understand), 12 (Associated with Circles), 13 (Rebellion and Hatred VS. Love and Unity, Good VS Bad Luck). If there is anything that I can relate to these in any way, I'll use it. 1 tends to be the least used for obvious God-mode reasons, 2 to anything halved, 3 sons of Noah or a small family unit, 10 normally involves places or organizations which can effect the development or creation of characters to fill roles, 12 like the division of the color wheel for eyes and 13 can help me with personalities with the different Zodiacs out there (though most think of only 12). That sterility can sometimes open up ideas that I wouldn’t have thought of before, because it limits and forces a redirect. I’ve also categorized creatures and their ways of creation, when in the character’s life the story starts, who their narrator is, grammar tenses, language, what has and hasn’t been tried, and what can I link, mingle or struggle some feature against. Admittedly, that’s only for certain characters; I pull one out of my ass when I feel like the plot is done like that, but I don’t have the heart to tell the other RPer that I’m not interested.

What do you guys think separates a "good" character from an "excellent" character? Like, in your opinion, where do the two differ and how do they differ?
The amount of amusement, whether it is believable or appealing, does it for me. Broad, I know.