Do I need a hardware midi controller in order to use Mixcraft's virtual instruments?

No you do not need a hardware midi controller to use virtual instruments with Mixcraft. If you're using Mixcraft 5 or above, click on the View menu and select "Musical Typing" to bring up a virtual keyboard that allows you to use your computer's typing keyboard to play notes on an instrument track and also adjust things like pitch bend and modulation.

For Mixcraft 4 users, if you do not have a midi enabled keyboard or other controller, you can use a virtual midi controller plugin, allowing you to play with your qwerty keyboard! Here are some examples:
Pablosoft Virtual Piano - VMCI - KB Piano

You can also import .mid files and adjust them using your mouse. A great example of using .mid files with Mixcraft could be importing a wav file of you playing guitar into software such as TS Audio-To-Midi and exporting it as a .mid file to use with Mixcraft.