What do the dots mean in HN.CO.CH3 connected to the second carbon of N- Acetylglucosamine? And what do the N and acetyl indicate?
These are not dots. They actually are single bonds though I do not know why they are printed that way. As such, they should be represented by a half-long dash (called EN DASH in Unicode).

In the name N-acetylglucosamine, acetyl means that a hydrogen atom has been replaced an acetyl group (i.e. –CO–CH3) and that the replacement occurred on the nitrogen (aka "N") atom.

Overall, it means something like: "consider glucosamine but replace one hydrogen on the nitrogen atom by an acetyl group". This is the standard "substitutive naming" defined by the IUPAC.