Rules scheduler reacting on last comment? I have a content type with comments activated and would like to have a rule that triggers a component when there is no new comments posted after a week. The component works as designed with rules scheduler, but I am having problems with creating a rule.

I have tried to create a rule that reacts on the event "After saving new comment". However, without proper conditions every comment will be scheduled to trigger the component one week after is is posted. The rule needs to overwrite existing scheduled actions if a new comment is posted on the same node. How can I achieve this?
To my knowledge, there is nothing in Rules to "overwrite existing scheduled actions" (as in your question). However, by every time attempting to perform an appropriate delete of an already scheduled rule, prior to scheduling a new rule, you achieve a similar result. And such attempt just gets ignored if there was no scheduled rule yet. Read on for more details ...

Have a look at my answer to "Rule to store user&#39;s last post date and scheduled rule based 30 day reminder" for an illustration about how to delete scheduled tasks, using the "schedule_delete". As explain in that answer: the schedule_delete that is part of this rule is to ensure that previously "scheduled" reminders will get removed when updating the data field (so that it only triggers 1 reminder, and with the most recent date).

To make this work (that you actually indicate the exact scheduled task to be deleted), you need to specify an appropriate "identifier", like "[account:name]" in my example. To understand how I know what in my case the identifier is of the task to be deleted, look at the way I specified my (new) scheduled task to be created: it is "identifier" : "[account:name]", which  is what I used as my identifier to schedule a task.

In your case, I think using the node's ID as part of the identifier would be a pretty good choice for such identifier.