Eddies are attached to the main flow. Is eddy and turbulence kind of loss of energy?

Your high school teacher's answer would be: Of course not! Energy is conserved. There is no such thing as "loss of energy" only transport and conversion.

More precisely, there is no such thing as "loss of energy", unless you are more specific and say "loss of energy to the open system", or "loss of kinetic energy". The latter expression is probably what you meant, i.e. "loss of kinetic energy". I wouldn't say eddies and turbulence "are" loss of kinetic energy because that's as illogical as "clouds are rain", but they are associated with such loss, which is really a conversion from kinetic to thermal energy at small scales.

I like the interpretation that "the kinetic energy is being converted to thermal energy at small scales". I should stop to use the illogical term "the energy loss".

Another question, will all the kinetic energy only be converted as heat for an unhindered free expanding jet?

Well, there is an easy answer to that question, but I don't know if it's of any significance to you: All energy is eventually converted to heat. I learned the term "heat death of the universe" in high school, as an expression that all the irreversible physical processes lead to ever increasing entropy and decreasing ordered (kinetic and potential) energy. The same will hold for your jet. Kinetic and potential energy is transferred from large scale motion to small scales (all the way through the cascade of turbulent eddies) and eventually converted to heat below the Kolmogorov scale. If you're looking at your jet running continuously in a finite size domain (open system), you'll inject kinetic and thermal energy to the domain at one boundary (jet) and your system will loose just as much energy (more thermal, less kinetic) through all the other boundaries. Depending on the size of your domain, you may not witness all conversion processes, i.e. the exit boundaries may be close enough to still see some kinetic energy passing through. But eventually even that will become heat.