Some excellent reference(for beginners)s for learning the meaning of vector operators used in Maxwell's equations;
(1) Berkeley Physics Course - vol. 2 by E M Purcel
(2) Introduction to Electrodynamics by D. J Griffiths
After reading from these two books, if you want to be an expert, read
(3)...
Your Question 1: What divergence really means w.r.t. a coordinate system?
My Answer: Divergence of vector results in a scalar. The same being defined at any arbitrary point and the divergence of a vector being a scalar, it remains same for any coordinate frame. A scalar always implies a...