Is there a circuit element which dissipates energy but does not act as a resistor?
If you will (hopefully) recall your complex impedance plane and the formula:
$$Z = R + jX$$
\$Z\$, obviously, is the impedance and it's a complex number because representing this as a complex number conveniently fits the mathematics.
\$R\$ is the &quot;real&quot; resistance and \$X\$ is the &quot;reactance&quot;.
In the real world \$R\$ comes from resistance elements and \$X\$ comes from inductance and capacitance.  This chart shows what this might look like plotted on the complex number plane:

While both \$R\$ and \$X\$ are measurable quantities, any amount along the imaginary axis is not dissipated as heat from the system.  It stays in the system indefinitely.  In an idea system it circulates or oscillates forever.  (There are real-world examples that approach this.  Think of the superconducting coil, or inductor, in an MRI machine.  This is a pure reactive load and an electrical current, once started when the machine is installed, basically circulates forever.  Well, not really forever but for a very long time.  There is effectively ZERO resistance in a superconductor to dissipate the energy.)
It's only along the real axis that energy gets dissipated, and this is what we call resistance.
In a real-world system there are many ways that energy gets removed from the system and the most common is heat.  But it could also be a motor that removes it as mechanical energy, an LED that removes it as light energy, a transducer/speaker that removes it as sound energy, etc.  These other things are not &quot;resistors&quot; but they have a component in the real direction that makes them look either fully or partially as a resistor for circuit analysis purposes.
So to answer your questions:

...is there a circuit element[s] which dissipates energy if a current flows
through it but is not a resistor

Yes, as noted above along with many many other devices that remove energy from a system.  But ALL of them have a Re component.  If they don't then they don't act like a resistor at all.

is there an energy sink which does not alter the properties of the
circuit

This is a VERY different question that is, IMHO, unrelated to your first question.  But the answer is NO, such a device does not exist.  In fact ANY device you place in a circuit alters the properties of that circuit in some way.