What are the pros and cons on installing a typical garage floodlight kit, inside your garage?
The immediate issue I see is that a floodlight is not great for lighting a room.  They cast harsh shadows, create a lot of glare if you look anywhere near their direction, and will leave plenty of dark areas in the room.  Of course, a few of those downsides could be fixed by just installing regular light bulbs rather than flood bulbs unless it has integrated LED floods.

Using a switch and the motion detector is possible if you are running new wiring to them.  You could have two switches where one powers the motion detector and the other powers the lights directly.  You could even use a three way switch if you never needed the light to be fully off (you could have always-on, or motion, but never totally off with one three way switch).

The other thing to consider is that some (many?) motion detection lights have a feature where they will stay on if you turn the switch off and on a few times.  This allows people to easily use the light in a passive motion mode or you can "force" it on from your back door by toggling the switch a few times.  Check your instruction manual - I know this used to be a popular feature but haven't had my own lights to try it on in some time.

As far as safety or code are concerned, I'm not aware of any issues that would prevent you from installing the light inside.