Pulling some highlights from Alves’ detailed answer:

Maxwell

Maxwell Equations should be best understood as:

1.Electric charges cause electric fields that converge/diverge to/from the charge: $$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0} $$

(In other words, charges attract/repel: $F_{1,2}= k_e \frac{q_1q_2 }{r^2}$)

2.Currents cause magnetic fields that curl around the current: $$\underbrace{\nabla {\times} \vec{B} = \mu_0 \vec{J}}~\text{ } ~(+ \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t})$$

(In other words, currents attract/repel: $F_{1,2}= \mu_0 \frac{\vec{I_1}\cdot\vec{I_2}L}{2\pi r}$)

3.Magnetic field lines always are closed, with no sources or drains of field: $$\nabla \cdot \vec{B} =0 $$

(Quite straightforward until here.)

4.The electric field curls around a variation of magnetic field: $$\nabla \times \vec{E} = \frac{-\partial \vec{B}}{\partial t}$$

This is a consequence, but during Maxwell is considered an additional relationship.

5.The magnetic field curls around variation in the electric field:

$$\underbrace{\nabla {\times} \vec{B} = \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t} }~\text{ } ~(+ \mu_0 \vec{J})$$

This is a consequence, but during Maxwell is considered an additional relationship.

From Jefimenko's equations we know that 4.,5. are not causal in either direction. The terms are due to changes in current generating both field changes.

Q1

Electric charges exist, and attract/repel. We can call the would-be force per unit-charge from them, the “electric field”.

True

No analogous “magnetic charges” exist. (Usually said as, “no magnetic monopoles”)

Partly True. Normally yes, and until recently was true everywhere. Now magnetic monopoles are an active line of research in both Particle Physics and Condensed Matter Physics.

In addition to charges, electric fields can also be made from the magnetic field changing at that point.

Not Technically True Maxwell describes relationships. The Jefimenko Equations give electric and magnetic fields as two separate functions, of charges, currents, and their derivatives.. only. This shows that Maxwell Equations are useful, tractable relationships. But the causes of fields are currents and charges and their variations. Jefimenko is based only on time-variation of the electrostatic Coulomb’s law, and the magetostatic Biot-Savat law.

Magnetic fields put force on moving charges

True, as a direct cause.

Q2

False, from all perspectives

Under Maxwell, the are truly separate terms. We can have current without any net charge, so that couldn’t be an electric field effect. And this statement is untrue using Maxwell: “One moving charged mass creates a magnetic field that can be determined just the same by looking at how that charge’s electric field is changing.” It must be seen as current and a time-varying field.

Q3 General

As mentioned, they are all ultimately just results of charges and currents and their derivatives. Jefimenko applied to electromagnetic statics (accounting for field travel delays at $c$).

Pulling some highlights from Alves’ detailed answer:

Q3: Maxwell Equations

The four Maxwell Equations (five relationships) are best understood as:

1.Electric charges cause electric fields that converge/diverge to/from the charge: $$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0} $$

(In other words, charges attract/repel: $F_{1,2}= k_e \frac{q_1q_2 }{r^2}$)

2.Currents cause magnetic fields that curl around the current: $$\underbrace{\nabla {\times} \vec{B} = \mu_0 \vec{J}}~\text{ } ~(+ \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t})$$

(In other words, currents attract/repel: $F_{1,2}= \mu_0 \frac{\vec{I_1}\cdot\vec{I_2}L}{2\pi r}$)

3.Magnetic field lines are always closed, with no sources or drains of field: $$\nabla \cdot \vec{B} =0 $$

(Quite straightforward until here.)

4.The electric field curls around changes in the magnetic field: $$\nabla \times \vec{E} = \frac{-\partial \vec{B}}{\partial t}$$

This is a consequence, but during Maxwell is considered an additional relationship.

5.The magnetic field curls around changes in the electric field:

$$\underbrace{\nabla {\times} \vec{B} = \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t} }~\text{ } ~(+ \mu_0 \vec{J})$$

This is a consequence, but during Maxwell is considered an additional relationship.

From Jefimenko's equations we know that 4., 5. are not causal - not from the curl to the derivative nor vice versa. The terms are due to current variations affecting each field individually. But without fields, the analysis is more difficult. If fields (Maxwell) are used, the terms in 2 and 5 must both be included.

Q1

A. Electric charges exist, and attract/repel. We can call the would-be force per unit-charge from them, the “electric field”.

True, and furthermore currents also attract/repel. We can call the would-be force from a current on another current if it was present, the “magnetic field”.

B. No monopole “magnetic charges” exist?

Partly True. Normally yes, and until recently was true everywhere. Now magnetic monopoles are an active line of research in both Particle Physics and Condensed Matter Physics.

C. In addition to charges, electric fields can also be made from the magnetic field changing at that point?

Not Technically True See Q3

D. Magnetic fields put force on moving charges

True, and as a direct cause. Currents put forces on other currents

Q2

False, from all perspectives

Under Maxwell, the effect on $B$ from current and $\frac{\partial \vec{E}}{\partial t}$ are separate terms. Both aspects must be considered.