Beginner: autofocus trouble

As you suggested, you may be too close to the subject or there may not be sufficient light for the camera to focus.  The minimum focusing distance depends on the individual lens and its focal length (i.e.the amount of zoom).  For instance, you'll definitely have to stand futher back when using the 50-200 than with the 20-50.

I am sure there must be specifications somewhere but I just tried my 50-200mm and could focus down to about 2 ft at 50mm focal length.  At 200mm, it required at least 5 or 6 ft to focus.  I found that sometimes I needed to get a vertical edge in the frame for it to lock onto.  This was indoors in poor light.

Be aware that mirrorless cameras are not good at focusing in poor light.  The NX series are about average in that respect.  However there are a couple of things you can do to help.  Firstly, make sure autofocus is set to "Single AF", not "Continuous AF".   Secondly, try setting AF Area to "Multi AF" (page 68 of the manual) or, if using "Selection AF", try increasing the AF area to its maximum size (page 67 of the manual).

In good light outdoors, focusing shouldn't be a problem and then you may want to do the opposite by setting to "Selection AF" and reducing the AF area to its minimum size so that it will focus precisely on the item you intend. (e.g. the eye of a bird or small animal).

To ensure you are not too close, try standing right across the room from the subject.  If you can focus from there, move a bit closer and try again.   Keep doing that until you have established the minimum focusing distance.