Hi and welcome,
To answer your last question first, although routers are designed to be left running continuously, there's no reason why you shouldn't turn yours off when it isn't being used, so long as you don't do this too frequently (e.g. more than once an hour). The danger with switching it on and off frequently is that DLM might interpret this as an unstable connection, which could result in your target noise margin being raised to stabilise it, which would reduce your connection speed. But this would normally require several interruptions in an hour, so once an hour or less shouldn't cause any problem.
However, all this shouldn't be necessary. As your DECT phone is double filtered, and your router's wireless interface is disabled, all should be well. Possible things to look at are:
- Does the standard corded phone show this noise effect when plugged into the socket used by the DECT phone?
- Do you have some different types of filter which you could try for the DECT phone?
- Is there any possibility of trying a completely different model of router?
