What is the state of actin-myosin in my biceps after I have flexed my arm?
When I've totally flexed my arm, are the actinomyosin left in this contracted state?

Yes, the sum of the length of all sarcomeres in series determine the length of the muscle.

So do they remain in this contracted state? Does the myosin head attach to the actin all this time?

Yes, it stays attached.

If it leave the actin, does the myosin snap back to its original position and relieve the tension/comeback to original length?

It doesn't really 'snap' back, it 'walks' back over the actin. 

Does it require any energy expenditure? 

Yes, the myosin heads require ATP to 'walk' back as well. If ATP is depleted cannot walk back, as is the case with rigor mortis (https://en.wikipedia.org/wiki/Rigor_mortis).

What is the state of the actinomyosin if left in a half flexed state? By state, I mean, the stage of the cross-bridge cycle

Myosin will partly overlap with the actin, but not completely. But this has nothing to do with the cross-bridge cycle. The myosin heads need to complete several cross-bridge cycles to fully contract the sarcomere. 

For further reading, the Wikipedia page on the sliding filament model is a good start: https://en.wikipedia.org/wiki/Sliding_filament_theory