When you look at the sensor can you see a blue-green coloured piece of glass mounted directly on top of the sensor? This is often seen on a lot of colour cctv type cameras.
If so, then this will be an IR cut filter so no additional filter should be needed.
The answer to your second question is no provided it really is just plain glass. “plain glass” will transmit most of the IR light in the range that silicon based sensors work. Most IR cut filters are this blue green colour I mentioned to simulated a broadly similar photopic eye response on a bare Si sensor. For example a Schott BG18 or maybe a broader pass Schott KG1 or equivalent.