What is the purpose of negative frequencies?
It's not a dumb question. In the case of your graph, the frequency is negative with respect to the centre frequency. So if centre frequency is 10MHz, and we talk about the 3dB points being +/-1MHz, they are 9 and 11MHz.
If you want to put a 100MHz square wave through an opamp, you will indeed need a bandwidth much more than 100MHz. Square waves have odd harmonics, so you need to pass frequencies of 300MHz, 500MHz and so on. The more of these you get through, the better the shape of the square wave will be.