Are there issues with the trickle charges and alternators??
Usually you would not charge when on the car as it screws the alternator over, of courses you can disconnect the4e red lead.
Solar panels only give max output when the sun shining bright and strong (mid summer) and is 90deg to the panel, all other times its lower, often much lower which is why on your house roof panels performance is naff if you live north of london with an average angle pitch roof.