With my air, usually start the mount, do a Cold Start, and then start the air and connect.? I use USB, by the way.??
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As far as guiding. I have never got numbers that low so can't give you much advice.? I will say it's very sensitive to calibration, and the Air will sometimes accept a wonky calibration.? ?So youbsre on the right track by re calibrating when guiding is strange.?
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For the go-to, those last few arc minutes of slew happen slowly.? You may not think the mount is moving, but it's going very slow to center up.? Just wait a few 10s of seconds.? I think you can also adjust the speed of those moves in the hand controller.??
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For homing...did you set the home position via the hand control or web interface???
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Also, mine will never confirm back to the air that it reached home.? For that reason, if I am doing more than one target in a night I will go directly between them instead of home in between.? ?
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I don't know how to directly answer your last question.? But my understanding is that the Air uses its location and time settings for the sky atlas.? Sends coordinates of the target to the mount, which then uses its location time and understanding of its current pointing to calculate the move.? So if it's going to the wrong side of the sky or pointing at the ground that usually means the time or location is wrong somewhere, or a clutch slipped or something where the mount is not physically pointing where the controller thinks it is.?
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Brian