No.
Kirchhoff's laws give relations that stem from the topology of the circuit --- how the components are connected. But they don't take any account of what kind of components are making those connections.
So you also need to have some information about the behavior of the elements. For example, an ideal resistor passes a current proportional to the voltage applied to it (a relationship called Ohm's Law). Or that an ideal voltage source provides a fixed voltage, allowing any amount of current to pass through it. As DanielSank reminded me, the equations describing the individual circuit elements are called constitutive relations.
With either KCL or KVL and the equations describing the components making up the branches of the circuit, you can solve any realistic circuit. This is called mesh analysis when done with KVL, or nodal analysis when using KCL.
It's also possible to draw a nonsense circuit that can't be solved by any method at all --- for example with two different-value voltage sources connected in parallel. These "circuits" are simply logical contradictions, not modeling any real physical circuit, so there's no loss by not being able to solve them.
Another limitation, KCL and KVL apply only to lumped circuits. That is, circuits whose physical dimensions are much smaller than the wavelengths associated with the highest frequency signal present in the circuit. In large circuits you might see effects like radiation or transmission line delay that are not modeled by straightforward application of Kirchhoff's laws, although it is in many cases possible to produce an adequate equivalent lumped element model for distributed circuit elements to allow Kirchhoff's laws to be applied to the rest of the circuit they're connected to.
I should also add, that while linear circuits (composed of voltage sources, current sources, linear resistors, and linear controlled sources) can be solved by straightforward application of linear algebra to the KVL/KCL equations and the constitutive relations, it's possible to construct nonlinear circuits that are extremely difficult to solve, and for any particular numerical solution technique there's likely to be some circuit for which it fails.
Yes, Kirchhoff's voltage law (KVL):
Sum of voltage drops across all elements connected via perfect conducting wire in series in to a closed circuit is zero.
is valid for lumped element RLC circuits, so also for inductors (for currents that do not change too fast, so voltage can be measured in practice). In practical circuits designed not to radiate, voltage can be measured across any element and KVL can be validated experimentally. It is valid for common frequencies, up to hundreds of MHz and even higher to GHz range if parasitic elements are added to the model.
The whole theory of RLC circuits with harmonic voltage sources is derived from KVL being valid all the time, while currents and voltages change.
Some people say Kirchhoff's law is not valid for a circuit with an inductor, since $\oint \mathbf E \cdot d \mathbf s \neq 0$ if ideal inductor is in the circuit. However, that is actually not a problem for KVL, because KVL is formulated using voltage drops, not integrals of total electric field. Voltage drop across inductor may be non-zero, even if total electric field in the wire is zero, because the drop is defined not by integral of total electric field, but by integral of electrostatic component of that field.
Best Answer
Both statements, which I assume address statement 1 of Kirchhoff' voltage law, are correct and essentially equivalent.
Your first statement given mathematically is
$$\sum V=0$$
Stated this way the term "algebraic sum" is essential since voltage rises are assigned positive values and voltage drops are negative values, requiring an algebraic sum.
Your second statement mathematically is
$$\sum V_{rises}=\sum V_{drops}$$
Written this way, it isn't even necessary to say "algebraic sum" in a verbal description of the equation, because all values of the voltage changes on each side of the equation are positive. Then
$$\sum V_{rises}-\sum V_{drops}=0$$ and
$$\sum V_{drops}-\sum V_{rises}=0$$
In either case the important thing is to be consistent in applying the rules for assigning voltage polarities across the circuit elements, which establishes what is a rise and what is a drop.
Regarding statement 2 of the law, I don't much care for it. It could imply that as one moves around a circuit loop all the voltage changes across non emf elements are drops and all emfs are rises. It depends on the direction chosen for the loop current (which is often initially arbitrarily assigned). What's more, a circuit element (e.g. resistor) that is in common between two circuit loops may contribute a voltage rise or drop in one loop, depending on the directions of the currents in the loops.
Hope this helps.