Can I extend/apply Schengen visa while in Switzerland?

Having scanned through the website, I noticed that the questions usually ask for extension of the Schengen 'C' visa after its validity date or the 90 days are up.

For my case however, I currently have a Schengen 'C' visa that is valid till 1st July. Now, I will be going to Switzerland for an exchange program so I have a 'D' visa as well -> for which later on I will receive a residence permit. So in effect, two Schengen visas (C and D).

To my understanding (anecdotally from others who have gone through it), the residence permit will expire when the school's official term ends (10th July). I, however, wish to travel a bit more in Schengen. Now since my 'C' visa expires 1st July and my residence permit (regardless of its validity date) will expire on 10th July, if I wish to travel within Schengen after my school term.

Is it possible to:

1) Extend the 'C' visa -> I will not have used up its 90 days. I am only using up about one week for a short trip this January and my subsequent stays in Switzerland will fall under the 'D' visa [and later the residence permit] and hence not count towards the 90/180?

2) if 1) is not possible, is it possible to apply for another Schengen visa while I am still in Europe? Seeing that I will still have a valid residence permit from Switzerland, would that constitute as my being a resident? (The problem being the permit means I do not need a visa to travel but even if it's validity is 3 months away, it could expire when my school term ends.)

3) Alternatively, could I request for the residence permit to be extended seeing that the rental lease for my accommodation doesn't end till about 21st July?

Edit: Just so it's clear I am a non-EU national and I require a visa to enter Schengen zone.