You are correct. Bad attitude for an educator. Or, maybe it is not. Maybe by being hard on novices, we can weed out those that are not willing to do the work needed to be a quality machinist from those that play around at it and give the rest a bad reputation. You might want to refer to the USMC boot camp. In days of old (30+ years ago), an entry level machinist (called an apprentice) would be partnered with one or more journeyman machinist for approximately 4 or more years of on-the-job training before they themselves would be recognized as a journeyman. During this time, these novices would be teased and harassed and generally hazed to see if they could stand up to the demands of working as a machinist.
A water separator has limits on how much moisture it can remove. Check the specs. A water separator will never work as well as a drier/dehumidifier. Even a drier/dehumidifier will have limits. The more capacity for water removal, the more it will cost. Putting traps in at air use connection points offers a way to drain water that accumulates in the air lines periodically. Most shops do not even drain their air tanks daily.
For cooling and chip removal, you have several options: use nothing, use air blast, use cold air gun, use mist coolant, use flood coolant, use high pressure flood coolant. Since you have an open knee mill configuration, high pressure flood is not a good idea at all. Depending on exact machining conditions, any one of the others is a viable option. As far as exactly what coolant to use, there are several that work well as general coolants. Contact your local distributor for recommendations and price options. Most go with synthetics and semi-synthetics these days because they are more bio-stable. You will also have to determine if yourself or anyone in your shop has any allergies triggered by any specific coolant products. Some people develop rashes or skin conditions from some coolants, but not others. The same for respiratory problems from atomized coolant. Some can develop asthma-like symptoms.
Being a good, quality machinist is not cheap. I probably have $3000-$4000 of personal hand tools in my tool box, and I do not have enough. I usually add another $100-$500 of personal tools per year. That does not count consumables (cutting tools, coolant, sand paper, etc.)
Have I become the grumpy old guy? Yup. I went from a college education as a drafter (Engineering and Drafting Technology) to quality inspector to machinist to
CNC programmer in about 3-1/2 years, because I applied myself and read every technical publication I could get my hands on and watched others and took literal notes and asked a lot of questions. And, after over 17 years in the machining and manufacturing industry, I have become weary of people coming into this industry and calling themselves machinist but could not machine their way out of a paper bag. I'll shut up now. Enjoy.