You raised several questions, so I will give my thoughts on them in order:
1) Sitting in Lotus in Yin Yoga before Shavasana.
There is certainly nothing wrong with Lotus pose per se, but it is not part of the normal Yin Yoga lexicon of postures. One reason for that is, most people can't do Lotus--it is what I have termed a "high-risk/low-reward pose". (See my article
Lotus Pose: Destroyer of Disease, or Destroyer of Knees?.) If you have the hips for the pose and there is no discomfort in sitting in Lotus, go ahead! But, for most students, there is more danger in trying to achieve this pose than simply sitting cross-legged.
If you do decide to sit in Lotus during your Yin Yoga practice, there is no need to engage pelvic floor muscles, no need for bandhas or special pranayama. Yin is passive, allowing, yielding...don't try to do anything muscularly, but rather allow the postures to do the work.
2) Should the pelvic floor/lower abdomen be engaged while meditating?
It depends upon the style of meditation you are performing. In any of the Buddhist styles I have been taught, there has never been any direction to engage any muscles: just sit tall, solid, and relaxed--as long as relaxing doesn't lead to slumping. In several yogic styles of meditation, there can be some rigidity in the body and specific breathing patterns advised. These directions should come from your teacher, however, who will have specific reasons for requesting these states.
3) How to counteract hours of sitting?
I have talked about the dangers of sitting in this short preview video
Death by Desk. Perhaps I can ask you to watch it, rather than repeat it all here. But, in general, when the body is held in one posture for a long time, we need to move it in other directions. If you are hunched forward all day, do backbends. For example, Sphinx or Seal Pose, or Saddle Pose with the arms overhead may work really well for you. Twists can also be great.
Cheers!
Bernie