1) Tape thickness is determined by the theme.
Look at api/scripts/themes.js - you can set the tape height (and you need to adjust the track height too).
Putting the label inside the track requires customizing the Timeline.OriginalEventPainter.paintPreciseDurationEvent method.
Basically, you just need to change the position of the label:
var labelTop = Math.round(metrics.trackOffset + track * metrics.trackIncrement);
and increase the thickness of the tape.
2) You should be able to do this by setting a null url for the image in the theme, and using the .timeline-event-icon class to set the background image sprite for the icon's div.
3) No, Timeline does not support this by default. You would need to do some customized javascript. I think there was some problem with timeline not correctly drawing duration events that were longer than 5x the width of their containing band.
--Mike