Exposure. Contrary to the conventional wisdom I don't think you should necessarily lock exposure when shooting panoramas. Instead use a metering mode that considers the whole scene (not spot metering), or shoot manual, and get a lot of overlap between images. If you do this the exposure shouldn't vary too much between adjacent shots.

The idea of locking exposure to make images match isn't necessary with current panorama stitching software, which after aligning the images is able to smooth out any changes in brightness.

The problem with locking exposure is that for many scenes there is no single exposure that is correct for the whole range of your panorama, especially if you pan near or past the sun. You have to compromise and accept a level of over exposure on one end and underexposure on the other end. Or you have to shoot multiple exposures for each position and use HDR. Arguably this is the outright best approach but it's a lot more work to good results.

Before I get downvoted it's worth stating that common sense should still be used and if the exposure is jumping around all over the place or the cameras metering isn't doing the job it should be locked.

Focus and aperture should still be locked, however as you can't blend depth of field and blur like you can blend brightness. You state:

Similar questions apply to focus, if you lock focus for a particular shot, can you be sure that others will not be out of focus?

Panoramas aren't usually taken of a single subject, but a whole scene or vista, so something will be in focus in every frame. However using a wide lens and narrow aperture like f/11 and the hyperfocal distance largely mitigates and focus issues.

ISO and shutter speed. In the ideal case you're shooting a static scene using a tripod, in which case set the ISO to the lowest value in order to use a longer shutter speed to capture as much light as you can. Otherwise you might have to chose shutter speed and ISO according to subject / camera motion just as you would if you weren't shooting a panorama. The important thing is you don't absolutely need to lock ISO or shutter speed, small variations wont be a problem, you need want to make sure adjacent images are similar with respect to noise and motion blur.

White balance. Ideally you should be shooting RAW since you are inevitably going to be processing your images. If not, the same advice applies as to exposure.

Focal length should be locked unless you really know what you are doing and are creating a panorama with a particular project in mind.