Sounds like focus operates when you press the shutter which is normal. The camera will only try to focus when you press the focus button (which is usually set as half pressing down the shutter button. A full press with activate the shutter to take the photo). You can separate the focus from the shutter button to another button but I’m not sure if the D3200 has an AF-on button to set it to.
Just remember focus action on the auto focus is dependent on the focus mode:
AF-S means the camera will achieve focus and lock to that focus when you press the focus button.
AF-C means the camera will continuously try to focus when the focus button is pressed.
Zooming in will likely change the focus point so you have to operate the focus system again to bring it back into focus after zooming in or out. The zooming action doesn’t cause the camera to refocus unless you tell the camera to focus.