One question, May I pay my debt when I want (after playing few market for example and just before playing a storryteller) ?
You can pay off Debt tokens in your Buy phase, before and/or after buying cards, at $1 per token.
This is why Capital's last clause is needed; it allows paying off Debt during cleanup.
Because of that clause, I suspect that there will be some card that cares directly about how much debt you have or whether you have debt. Maybe something that multiplies opponents' debt. Otherwise paying off debt early would be unnecessary, since the next time you could buy a card, you could just pay off the debt then.
(Except Black Market, but that's hardly a reason for that whole line of text.)