I see no icons / I see only "?" icons
Your icons are not properly installed. These are now part of the e17 tree, so if you have that installed it will more likely work.
You must put _all_ your icons (for matching running apps) into ~/.e/e/applications/all - these will be .eap files (try eap_edit)
For identifying icons you want to remain in the launcher area you need to setup a .order file in ~/.e/e/applications/bar/engage.
For information on creating these files or their formats check the ever changing e17 hints pages at get-e.org
Engage seems not to behave so well with E17 - what have I done wrong?
Nothing wrong. Engage is currently not entirely compatible with e17.
Engage is being ported to e17 modules as I type and hopefully it will be fantastic any time soon...
For those who want a sneak preview try the latest engage, make (after e17 is installed) and load the module.so installed into e17 using the configuration panel or enlightenment_remote