In statistical mechanics and thermodynamics, thermal equilibrium between two systems doesn't require persistent contact between two systems, it merely means that if an energy-transmitting path is opened between them, then nothing will change in their macroscopic properties.
In statistical mechanics this is a bit subtle. While it is true that opening the path changes the future microscopic behaviour, and the amount of energy on each system fluctuates as they swap energy back and forth, it doesn't matter since we don't know what the initial energies were to start with. It also means that for two systems to be in thermal equilibrium, their energy probability distributions need to be set up very carefully so that they are insensitive to the process of energy exchange. But this sort of "careful" probability distribution is guaranteed if both have a Boltzmann distribution with the same parameter! And so, in statistical mechanics when we say something has temperature $T$, what we really mean is it has Boltzmann distribution with parameter $T$.
In thermodynamics when we speak of the system's energy we are always referring to average energy. Heat exchanges always refer to average energy exchanges. So heat exchange is strictly zero in thermal equilibrium. But in statistical mechanics the term "energy" could refer to either the real energy (which is a "microscopic" variable-we cannot actually know it) or the average energy. In statistical mechanics it's good to be precise about the distinction.
So the answer to 1 is yes, two isolated systems can indeed be in thermal equilibrium with each other even if they never met, provided they have somehow been given the same temperature (both having Boltzmann distributions with same $T$).
Answering 2, note what I said about heat exchange above... even though heat exchange is zero, the systems do randomly exchange energy.