You do not have to do a three star alignment every time. The message concerning NPE is not an error or really (in my opinion) even a caution. It's simply informational in that it lets you know it is reusing data that shouldn't have changed much since the last time you used your telescope. I sort of question why SkyWatcher used the word "Caution" in the message instead of "FYI:" or something less dramatic.
Your second question about decreasing accuracy of GoTos as you move around the sky can be caused by one of two problems (or both).
The first issue is physical polar alignment of the mount. The better polar aligned you are, the better GoTos will be after doing you star alignment. You should be in pretty good shape if you polar align with the polar scope and are very careful with getting Polaris in the correct place on the reticle (after carefully orienting the polar scope).
You can improve on the physical polar alignment of the mount by using the HandBox Polar Alignment assistant. (See section 11.3 of the SynScan Users Manual.)
The second issue that can affect GoTos is the choice of stars you use during your three star alignment as well as how you center them. There is a rather detailed description of how to best choose alignment stars in the SynScan Users Manual. See section 3.7 of the appropriate manual. When performing the star alignment procedure, be sure to use the "finish centering with the up and right buttons" advice. (See section 3.6). (Below are links to the manuals for both the Version 3 HandBox (older model) and the newer Version 4 HandBox. (Both HandBox version have exactly the same functionality.)
Version 4 HandBox
Version 3 HandBox
Section 3.7.3 in particular, gives guidelines on selecting the best possible stars for a three star alignment. You can use any stars visible from your location but following these guidelines will give better pointing accuracy across the sky than just choosing any three random alignment stars.
I realize all this is a lot to remember. You can use the scope without doing any of this and GoTos will be generally OK. If you want the best possible GoTos from the HandBox, try to learn these "Best Practices Rules". After a while they will become second nature to you.
For the ultimate in pointing accuracy, you can consider using EQMOD software. This has the disadvantage of requiring you to take a laptop when observing although it does add the feature (among many advantages) of being able to run a planetarium program to see the sky on the screen and then doing GoTos by pointing and clicking on the map of the sky.