Can I zoom in, manual focus, then zoom out?
To answer your second question:

You can only use the zoom in, focus, zoom out if the lens is parfocal. Normally a parfocal zoom lens starts at 3000-4000 USD, thus I highly doubt the lens in this camera is parfocal.

Then again, how much of an issue this will be depends entirely on the lens, perhaps it won't loose a lot of focus or it will loose a lot of focus when you zoom out.

I'm not familiar enough with the camera to really answer your first question, but in general terms manual focus is the only way to lock focus. However, modern auto focus in certain cameras keep focus very well, but it isn't locked as such.