So the Shadow Arts ability is listed as:

Starting when you choose this tradition at 3rd level, you can use your ki to duplicate the effects of certain spells. As an action, you can spend 2 ki points to cast darkness, darkvision, pass without trace, or silence, without providing material components. Additionally, you gain the minor illusion cantrip if you don’t already know it.

Does that mean to use the minor illusion cantrip, you are spending a ki point?

You don't spend ki to cast minor illusion. If you had to, it'd be listed with the other spells or it'd have a different ki cost listed.

^Exactly what InquisitiveCoder said.  "as an action, you can spend 2 ki points to cast darkness, darkvision, pass without trace, or silence, without providing material components".  Just those spells.  "Additionally, you gain the minor illusion cantrip if you don't already know it".  No stipulations, ki usage, or anything, you just gain the minor illusion cantrip if you don't already know it.

The character I am hoping to play in Waterdep Dragon Heist and the follow up adventure is a Variant Human Monk, and during the adventures I plan on Multiclassing to Sorcer for the Shadow Magic subclass to level 3.

I agree.  I do not read it as costing Ki to cast the MI cantrip - "in addition you gain.." 

Sorry, I am a super noob here, but as I read the shadow arts ability that is listed.  I would spend 2 ki points to use any of those shadow arts at no material component cost other than MI not costing any KI but materials.  So does that mean I can cast the other shadow arts with components and not use ki points?  

No, you do not actually learn to cast them as normal, you only learn to duplicate their effects using Ki.

I think I understand.  I was also told spell casting uses spell slots when the monk doesn't use spell slots.  Thanks for your help.