I'll attempt to answer the questions primarily as a depression-anxiety sufferer.

"What are the essential qualities you look for in a friend?"
Kindness.

"What would be a deal breaker when you would have to end contact?"
Oh, I hope this wouldn't happen. A "deal breaker" might be a development in the relationship that posed a threat of harm to myself or the friend.

"And for more minor “infractions” etc, would you try to discuss things respectfully before ending contact?"
Yes. In view of my extreme hesitation to confront anyone, I probably would approach the topic indirectly and with great caution.

"Also, are you a good friend to yourself, or do you try to be?"
I seek to think about myself little. On the other hand, I do think much about my health, mental and physical, and attempt to discover what is "healthy" for me and pursue it.