Hi there,
Most of this seems to come down to personal preference but in my opinion...
Manual FUE is the best option of the two
Definitely not robotic
Density measures like a surgeon measuring the thickness of the caliber of your hair is so that they can work out what level of coverage you will achieve based on your hairs characteristics
How do you judge the skill level of a surgeon? Results my friend, results. Look at as many examples of hair transplants as you can, good results and bad, list your top surgeons and narrow it down based on how often you see a solid to strong result that you would wish them to replicate based on your own hair loss pattern and goals.