Not like you want...
When it's off the permanent Paradox point from the buff (if applicable in the first place) is gone.
No. Only a spell that doesn't remain at all will not incur a permanent paradox. You'd need to re-cast the spell to get this benefit.
Or you hang the spell and only complete it at a later time, using Time and/or Prime as additional spheres. This is an almost-pre-cast spell prepared in advance, granting its benefits once you trigger it without permanent paradox... but it will end as usual once either the runtime is up, or its effect happened.
When it's off there is no resonance from the buff radiating from me (so no way to see magic on me using senses spells, including sphere-based senses).
No. A dormant effect, such as cybernetics turned off or down, will always be detectable as magickal in some way or another. If the source is a worn item, not wearing it and having it stored somewhere makes it undetectable but unuseful. A hung spell similarly is very noticeable, as it is technically a suspended magick just waiting for a keyword.
As JRodge01 suggests, you could also work with simple triggers to force a long-lasting spell into a dormant state, but that would not be undetectable, it would be running very much at full power all the time, only its effects are suppressed.
When it's off, effects of the spell don't apply (I can think of several effects that might be good or bad, depending on situation).
Yes, you can have this. Turning off a spell can be done in two way: fully canceling it, or not using the item it is applied to. The latter is usually an artifact or invention, but also could be a genetic modification or other thing.
As a simple example, let's take a girdle of giant strength: you can choose not to wear it. Or wear it but not activate it. Only once you activate it you benefit from its bonus. Usually, such items have an activation roll.