Regarding the presence of primer sequences on reads after primer removal using cutadapt

I'd suggest reading the plugin help text and the cutadapt documentation regarding adapter types. There are also a few examples of this in the forum. See:

and

They should always be removed as the primers can make sequences appear more similar to each other then they actually are (and contribute to chimera checking problems). Remember that the PCR primers can bind with a reasonable amount of mismatches and become part of the sequenced amplicon itself. That is, due to the amplicon being PCR amplified each cycle and then finally sequenced. The area to which the primer binds will be the sequence of the primer itself, which may not necessarily be the actual sequence from the organism you are sequencing. Hence it is a good idea to remove the primer sequence prior to constructing OTUs/ESV, and phylogenies.

I am not sure why you are still observing primers.