Is it possible to get a (custom?) skill to configure a checklist Alexa would voice out?
Yes. It would probably be relatively easy to develop a skill to do this yourself, if there aren't any available, but there are a few to-do list skills (e.g. Todoist or Any.do) if you didn't want to go through the hassle of developing your own skill. You may be interested in the Steps to Build a Custom Skill, which seems to be a useful guide to learn how to make a skill. You mentioned previously that you were happy to develop a solution if necessary—if that's still the case, and the to-do list isn't what you want, a custom skill is the way to go.
If possible when voicing a goodbye message ("I'm off, etc.")
You can override the built-in commands (e.g. "I'm leaving"), if you set the invocation name of your skill to the name of a built-in command. This works because there are three formats for invoking a skill:
“Alexa, Ask Daily Horoscopes for Gemini” (an
“Alexa, [open/start/ask/...] Daily Horoscopes” (a
LaunchRequest with a prefix, like 'start')
“Alexa, Daily Horoscopes” (a
LaunchRequest without any prefix).
It just happens that if you name your skill "I'm leaving", saying "Alexa, I'm leaving" happens to be a
LaunchRequest for your custom skill.
Be aware that you would not be able to publish this skill, since it overrides a built-in command (and Amazon wouldn't take very kindly to that!).
If possible I'd like to maintain different "checklists" for when I go to work, when I go dancing, etc. And each would be associated to a different checklist.
You could probably write this as an intent.
Alexa, I'm leaving for work.
Alexa, I'm leaving to go dancing.
You could set up an intent schema as I described here with an
AMAZON.LITERAL slot, and then your skill would be sent keywords like 'work' or 'dancing', which you could then use to decide which checklist to show. The rest of the problem is essentially loading the right checklist, and then returning the utterances for Alexa to say to you.
I suspect it'll be easier to figure out the exact problems you face once you start developing it—I find it hard to anticipate all the problems in advance, and hopefully it'll 'come together' a little as you go along. Good luck!