7D Doesn't Like to go Over 1/200

Another potential pitfall; you'll find the camera has more leeway if you use AV, not TV. In TV it's too easy to select a shutter speed and find the camera can't find a large/small enough aperture to make a correct exposure, and it's then very easy to miss the warning in the viewfinder. The converse is less likely in AV mode,and it's much easier to see the selected shutter speed and change the aperture if necessary.

As others have said, turn auto ISO OFF so that the camera does what you tell it to.

You'll never find hairs on a duck's egg, you will always find hairs on an ape. It is only the hairs on a gooseberry what stops it from being a grape.