Travelling with 2 Valid visa - Schengen 'C' & 'D'

So I'm a non-EU National, due to an upcoming trip in January I have a Schengen 'C' visa that was issued (validity from 5th January to 1st July for 90 days).

In February, I will be in Switzerland for an exchange program for 5 months & have been given a 3 month 'D' Visa (8th February to 7th May). It's only a 3 month validity because from my understanding, the 'D' visa for Switzerland serves only as an 'entry clearance' of sorts, it is the residence permit which will allow me to stay the full 5 months. [Unlike France where the 'D' visa lasts for the entire duration of an exchange]

Anyway, whilst my residence permit is processing, if I were to travel out of Switzerland (or even Schengen), at the border control for non-Schengen or random checks for intra-Schengen, will these 2 simultaneously valid visas be an issue ? Even though they are different types, they both allow travel within Schengen.

From my understanding, once I get my residence permit then my days spent in Switzerland will not count towards the 90/180. However, how do they know how much time I spent out of Switzerland (but within Schengen) ? Or is it based off the validity duration of the Residence permit ?

If so, let's say the permit is valid from 8 February to 8th June, does that mean that the 'C' visa will not be deemed to have been 'used' up till the expiry of my residence permit? so If i remain until 30th June, then my days under the 'C' visa will only start counting from 8th June to 30th June? as well as the days spent in January of course.

My question mainly stems for travels while both visas are valid (& especially when I get my residence permit but the 'C' visa is still valid - is that possible? or does the residence permit sort of annul the 'C' visa?).

Both the 'C' as well as the 'D' visas are multiple entries.