I hope I am reading your maps correctly.  Wells are a great way to help understand what is happening below the surface relative to groundwater and aquifers.  I don't know the geology or depths of the wells, but the values in figure 2 suggest to me elevations higher than the terrain, which is indicative of the wells drilled below a confined aquifer under some pressure.  If these readings are depths from the surface, my apologies, but seems very unusual to me..  As you have probably learned with Darcy[s Law, areas of higher water table head move toward areas of lower water table head.  What you see on ground surface with topographic lines is not always what is going on under the surface.  If you see there is an area of rapid lowering of water table, that might suggest that there is a spring either exposed to surface or flowing subsurface that is lowering that area much like a well pumping water out, or their could be faults and lineaments that move water or disperse.  By the water quality in the groundwater and the streams, you probably can detect with some study if the stream water is deep groundwater or more rain or shallow groundwater interflow.   I know enough as a hydrologist to know I may not know enough to answer all your questions or suggest what geology indicators you should be looking for to explain some of the readings.  The paper added is from the coastal plain, but the methods used separated the hydrograph by the source of the waters from rainfall to groundwater.  This coastal area has various deep confined aquifers, and some of them are under pressure and when well drills through them, water emerges without pumping sort of like an artesian well.  But there is also a surface unconfined water table that can vary due to somewhat impervious layering of marine terrace deposits.  You may be interested in their approach and understand that subsurface water can sometimes be defined by water quality differences.  If you are interested in karst terrain, our paper in researchgate on Springs of Missouri (~1975) also shows how spring water quality changes with flow rate in adjusting to rainfall events and subsurface storage change. 

Concerning sites 31, 30 and 34.  30 appears to be in a topographic depression (headwater stream channel) while the others near the ridges, so the lower reading at 30 suggests release of flow into the channel system to me (unsure where it might be but probably would look in vicinity of channel at or below your data point as a possible stream headwater source due to groundwater connection and that may help explain the 10-15 masl reduction in water table elevation at site 30 as compared to 31 and 34.  Reading the stream contour crenulations (indentations and extensions) to denote streams and ridge systems will help you evaluate the surface features and their likely reference to groundwater, whether it may be collecting and releasing in underground water in streams or storage and dispersing subsurface through head, hydraulic conductivity (Darcy's) along ridges.  When streams tap groundwater, the water can flow more freely. 

It was very interesting and informative discussion by Dr. William F. Hansen.

To understand and explain the maps, additional information is required. A hydro-geological (geological) cross-section with locations (including depth) of piezometers would help. (Are all piezometers in the same aquifer). It would also help to know the topography (e.g. from Google Earth) and scale of the map to know locations of rivers etc. that may be draining off. Also possible existing groundwater extractions should be known (or might influence the readings). This all provided the readings can be trusted and are also not influenced by any differences in density. I'm wondering how these observations can be trusted where the groundwater - e.g. in MAT07 or MAT 022 - seems to be elevated more than 10 m above surface level? How is this measured? Probably not in an open standpipe.

http://study.com/academy/lesson/factors-that-influence-groundwater-movement.html

http://dnr.mo.gov/geology/wrc/docs/WhyWaterLevelsChange.pdf?/env/wrc/docs/WhyWaterLevelsChange.pdf

The problems in interpretataion can come from the fact that maybe not all mesauring points (wells or piesometers) are in a same aquifer zones. The answer by John Lambert quite good explains what is necessary for interpretation. Based on my experiences, if on some locations you have several aquife zones, some of them with free groundwatérmsurface,,amd some of them under artesian presure, than you need double or triple piesometers to divide aquifer zones. Then it is possible to interpolate parameters. Always combine data from hydrogeological sections with map. See in my researchgatte profile some pictures in the artifle Interaction matrix method in hydrogeological analyses for coal mines. 

FACTORS AFFECTING GROUNDWATER FLUCTUATION BELOW GROUND SURFACE:

1. Subsurface geology.

2. Hydrologic properties of the subsurface material- Aquifer (unconfined, confined), aquiclude, 

3. Physical parameters of aquifers like transmissibility, storage co-efficient and specific yield.

4. Groundwater draft or extraction / pumping activities

5. Terrain slope & Groundwater gradient

6. Natural discharge through sub-surface discharge or spring discharges

7. Rainfall pattern- Intensity & Distribution

Others factors may include

i.) Climate change

2.) Subsurface geology

3.) Over-withdrawal of groundwater 

Geology and topography

Lithology and type of aquifer

spatial distribution of rainfalls

Human being activities related to water and soil (extraction)

A groundwater level whether it be the water table of an unconfined aquifer or the piezometric surface of a confined aquifer, indicates the elevation of atmospheric pressure of the aquifer. Any phenomenon that produces a change in pressure on groundwater will cause level to vary.  Difference between supply and withdrawal of groundwater cause levels to fluctuate.

There are three types of variation of groundwater levels-

1.Secular variation: Secular variation of groundwater levels are those extending over periods of several years or more. Associated with climatic changes.

2. Seasonal Variation: Groundwater levels shows a seasonal pattern of fluctuation. Associated with rainfall and irrigation.

3. Short-Term Variation: Groundwater level display short term fluctuation governed by the primary use of groundwater in locality. Associated with municipal water supply wells.

There are many factor which affect groundwater level fluctuation as mentioned below-

1. Rainfall

2. Evapotranspiration

3.Atmospheric pressure

4. Wind

5. Frost

6. Ocean tides

7. Urbanization

8. Earthquakes etc.

If want go in details please refer Groundwater Hydrology book (Third Edition), Authored by Todd and Mays,2005.

you should check if all water wells are drilled in the same aquifer. The variation of water level may be a result of stratified aquifer which can give different value of water level. 

Topography, soil characteristics and rate of water withdrawal also affect groundwater fluctuation