Can a model choose not to activate, or activate and do nothing? this of course most often would be beneficial when engaged and one does not wish to initiate and attack sequence.
As already said, you must activate every model, and if you're engaged you can not do nothing. But if you're free from opponent, you can do nothing if you want.
Can a lemure activate while engaged and do nothing? Mainly comes up when they have a vanishing spell and dont wish to use it yet. I see this as them moving 0 fathoms, but that is admittedly a stretch.
No a lemure must move anyway, as the book state it. But you can always move him by a few millimetres. But keep in mind that your opponent can hit him during his own activation.
Is a lemure even capable of initiating an attack sequence?
No. It's not written, but it's the effect of adding all rules about them.
Do other models still have to retreat to leave combat with a lemure?
Rules about retreat states "If, during the one-sided attack, the enemy is Harmless, the attack is cancelled and the retreating unit may use its retreat action to perform a Walk, Run, Attack, Charge, Shoot, or Concentration action."