When you ask:
So I was told in the physics class that the resistance in a parallel circuit is lesser than the resistance in a series circuit.
This question only applies when two resistors are connected in series, versus the same two resistors connected in parallel instead. It's important to understand that apples-to-apples comparisons can only be made when the circuits differ only in how the resistors are connected.
Now, given this, your next statement:
Why does that happen?
Convincing someones else "why" something is true in physics is a really tough job for anyone. However, I recommend sitting down with a calculator and calculating the total resistance of two $5 \Omega$ resistors in parallel, and then comparing that with the total resistance of two $5 \Omega$ resistors in series. Then repeat the calculations with $4 \Omega$ resistors, $10 \Omega$ resistors, and so forth until you convince yourself (as I originally did) that the statement must be true for all resistors.
You go on to ask the question:
Is this statement also true for circuits which have no resistors or resistance offering devices connected to them?
Circuits that have no resistance at all (on paper) have an infinite amount of current going through them (on paper). Trying to compare this situation with circuits that have resistance is a fairly meaningless comparison. If this is a homework question, I recommend answering "no" and then stating that these two situations cannot be meaningfully compared.
Lastly, you go on to ask:
And also from my calculations the total resistance in a parallel circuit is lesser than the resistances of any of the devices connected in the circuit.
Again, it might resolve the confusion is you simply tried out various resistor situations, did the calculations with a calculator until you realize that it must be true for all resistor values.