Suppose that we have 2 objects and both of them reached thermal equilibrium. Do the particles of the two objects still collide with each other? If so, do any of the collisions result in the transfer of energy between the two objects? Explain.
Would two gases count as objects? The particles have a distribution of velocities. If we mix the two gases there will be energy transfer from an atom or molecule of A to B. Over all there is no energy transfer from A to B. Now consider solids. There will be exchange of phonons which means energy when they are in thermal contact. There will however be no net transfer of energy. If they are metals, there will be heat exchange through electron collisions too. Transfer of energy will be bidirectional . Only on average there will be no energy transfer
Microscopically the particles of the two bodies are of course in motion. Motions do not cease just because the two bodies have the same temperature, this just means that they happen with the same averaged energy.
Even if each individual body is first of all in internal equilibrium itself, the kinetic energy of its particles obey to a statistical distribution, some have more some less. As such there will be plenty of collisions that transfer energy between particles within the same body but without no net change.
The same happens at the boundary between the two bodies. Plenty of collisions transfer energy from, say, A to B, while others do the opposite.
Thus, yes there are collisions but not overall energy exchange.
Related Q&As here Does heat transfer actually from high temperature to low temperature?
Yes, they collide if you mix them. Being in thermal equilibrium does not mean that no particle interactions, i.e. collisions, happen. It rather means that most of the particle have the same speed. Or maybe it was better to say that for each particle the same speed has the highest probability, independent of its location. But besides the macroscopic phenomenom of the temperature, microscopic collisions still (and frequently) happen.