CURRENT is the number of electrons that flow per second (specifically, one amp of current is a Couloub of electrons per second). If you drill a large hole and a small hole in a barrel of water, the CURRENT of water would be larger in the large hole.
VOLTAGE is the energy per electron (specifically, one volt is a Joule of energy per Coulomb of electrons). If you drill holes in the top and bottom of a barrel, the water will squirt out of the bottom hole more energetically (more voltage due to the potential energy of the water above it).
Please pardon the water analogies, but it is easier to consider tangible voltage and current to understand what is happening.
A NODE is a place where wires meet. Thus, if three wires meet at a point, that point is called a node.
KCL is Kirchoff's Current Law. It says that the amount of current going into a node is zero (note: current leaving the node is negative). If it was not for KCL, electrons would enter a node and never come out, and there would be such a build up of current that the node would explode. So, electrons that go into a node must come out somewhere.
KVL is Kirchoff's Voltage Law. It says that the sum of all voltage drops in a loop must equal the source voltage. So, if you have a series string of ten Christmas lights, and each light has an equal resistance, you would have 1/10 of the voltage across each light. In a series loop, the current through all resistors is equal (in other words, all of the Christmas lights would have the same current).
Capacitors temporarily store voltage (in the form of an electric field), so they have reactance (that is like imaginary resistance).
Inductors temporarily store current (in the form of a magnetic field), so they also have reactance (like imaginary resistance).
ANSWER TO YOUR QUESTION:
In a resistor, there is no phase change between current and voltage (such a change only occurs with reactive components (capacitors, inductors, certain semiconductor circuits that emulate capacitors and inductors, and certain microstrip structures that emulate capacitors and inductors at high frequencies)).
So, since there is no change of phase, KCL and KVL don't depend on the relationship between current and voltage in a resistor.