The questions aren't specifics, just in general.  I've never grown it before and am wondering if there are any potential pitfalls/common hazards I should be aware of (too much moisture, not enough moisture, deficiencies, etc).  They'll be grown indoors under lights, of course.

I have several Moringa's and I can add that to make them full you will want to pinch off top growth AND prune the early stems back about half way.  Otherwise, they will be tall and lanky with few branches and leaves.
I would think growing a Moringa in a pot will be quite difficult in that Moringa's put out a deep tap root.  That deep Tap root is what makes them drought tolerant.  I wonder how the plant will fair without it.

I am not sure what eggs those are from, but agree to let nature take its course first.  A balanced garden is a healthy garden.

Regarding the Anthracnose; my mango's had (note past tense  ) severe anthracnose because they were uncared for as this property sat empty for four years before I purchased it.  I used a new earthfriendly product from Organic Labs http://www.organiclabs.com/Retail.html called Plant Doctor and the Anthracnose cleared up completely!
You can get it at Home Depot .. I also got their Fruit Maker as a folier spray of Potassium.  It was developed at Texas A&M as a form of Potassium that uptakes significantly more than granular.