Yes, the characteristics of the aquifer can be determined without a piezometer.

Using GIS and hydraulic analysis

Yes, we can determine the hydrodynamic characteristics of the aquifer by pumping test, and it is one of the best methods with excellent results. You can use Aquifer test software,

Why not? Yes. Various aquifer parameters including hydraulic conductivity, storativity, and transmissivity can be determined from a pumping well and that is the p[perfect method to determine these parameters for water supply production well.

Usually, only the transmissivity or hydraulic conductivity of the aquifer can be determined for simple Theis model for a quasi-stationary regime using the Jacob method. Storativity cannot be determined due to the skin effect of the borehole wall.

If the curve S-lgt has stabilized, then try the Dupuis equation for steady-state regime. Use the last points. The radius of influence of the well R can be found in multi-strength textbooks.

Usually, in any case, the error in the conductivity value does not exceed 30-40%.

It is best to use the model (aquifer, filter location, distance to river ...) that is closest to your design

Here's a link to some graphics related to determination of hydraulic properties. I have done a lot of these http://dudleybenton.altervista.org/projects/WellTest/index.html

Yes. This is one of the commonly used methods.

I agree with Alexei Lekhov. Without observations in another well or piezometer you only can estimate the transmissivity and the hydraulic conductivity. If you perform a pumping test with several changing of the values of discharge (at least 3) you can also estimate the parameters characteristic of the well. About the values of Storage coefficient usually we get meaningless values, even when they seem reasonable.

Yes. it is the most frequent method.

Alexei Lekhov has said it clearly..