We know that we do have composite particles (for example Atoms) made of fermions or bosons or mixture of them with fermionic or bosonic statistics. So why can't a gas of $2N$ fermions become a gas of $N$ bosons and condense to the lowest state at low temperature (just like what happens in superfluidity and superconductivity)?
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It can. This is exactly what happens when Helium-3 becomes superfluid. It's also what happens in superconductivity, which you mention in your question, when electrons combine into Cooper pairs.
Well, it's not exactly what you ask since neither liquid Helium-3 nor electrons are a gas. It's very unlikely a gas of fermions could pair up to form a gas of bosons because the energy required to disrupt the pair is typically very low, and requires temperatures at which the gas would liquify. The nearest to a gas would be a fermionic condensate, which was first made in 2004.
John Rennie
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