League-of-legends – How are “premade” lobbies matched against opponents

Currently the Answer is NO.

Once you click on "Save and Use" the masteries are saved to mastery page number X (Where X = 1-10).

I completely understand what you mean with using different summoner spells on the same champion role, so what I created was, different mastery pages for the same role each with a different combination of summoner spells, so for instance my mastery pages looks like:

The one last mastery page is left as a Configurable one during champion selection, so if someone else on my team has clairvoyance and I am playing a support champ, I can get instead of C.V flash or heal.

10 Mastery pages should be enough to customize your preferences.

EDIT:

especially since I then have to remember which one is "Mastery Page 4"

You can change the mastery page name by simply clicking the default name and when done hitting ENTER.

The short answer is no. You are always in a better position if you are using a champion whom you are good at playing.

If you pick a counter you are not good with, you will have to try and adapt your playstyle to a kit you don't know, create an item build path you haven't used and played with before, and try to figure out exactly "how" your kit counters their kit.

For instance, someone picking Talon mid vs a squishy AP mid would be at a serious disadvantage if they didn't understand how Talon's burst combo should be used. If you go in on Brand with no understanding of how to quickly get Talon's damage in before Brand can start his combo, you will die.

tl;dr: If you are trying to counter a lane, rely more on your ability to play a champion well than which kit counters your opponent.