Just to make sure that I am reading this right (and paraphrasing the rules):

Home Ground (10 karma): As per Street Grimoire, page 32, the awakened character ignores the background count of an area, and suffers only half the penalties to any changes due to temporary events.

Astral Hazing (-15 karma for Awakened): In short, you create a Rating 3 background count, a domain, in Essence meters around you. Likely to be 6m from your typical awakened character.

So, for a net gain of 5 karma from just these two qualities for an awakened changeling, one could become acclimated to their own haze?

It'd only work at the location that you picked for your Home Ground quality to take effect in. Probably would only be worth it if you expect to use your magic a lot at home. Which would at least make summoning spirits on your down time easier. But you might end up building up a bad rep in astral because you're forcing them in to background count they don't like.

It is a matter for GM adjudication. Personally, I would be inclined to treat astral hazing as a permanently-refreshing "change due to temporary events", since the background count is (assuming similar flavor text to SR4) continually being generated by the character's own darker emotions and negative feelings, rather than being the static impression left by negative past events.

Like DeathStrobe, I would limit the quality to a geographical area. Otherwise, everyone could just take their own immediate vicinity as the area, and be immune to background count everywhere they went.

My thoughts exactly.