Plenty of answers there to your first question. I would answer the second this way, but must stress that this is only my opinion and the way I see it. I'm not a 'professional', just an average guy who's been sawing and sharpening his own gear for 40+ years - that doesn't mean my opinions are right, more that I'm set in my ways!
The new cutter has a gullet that is a perfect fit for the recommended file. A perfect fit is always a Good Thing - the gullet is an arc that neatly matches the right-sized file. If you use a bigger file - ie: with a wider diameter - it will make that arc shallower, or flatter. Use a smaller file and you'll dig into the gullet, making it more pronounced and rounder. A smaller file will also only work on the side (vertical) edge of the cutter and miss the top, horizontal edge. If the file is too big, it will only sharpen the top edge, not the side - at least, to start with, until it's totally changed the shape of the gullet.
If you use the recommended file, a small proportion of the file, at the top, will actually be above the level of the cutter. This means that the file won't just work on the side edge of the cutter, but also on the top edge, so sharpening both at the same time. If we apply absolutely no upward or downward pressure, but only put pressure horizontally into the cutter, then with the recommended file we should maintain the original gullet shape and also sharpen both cutting edges equally. We are all likely to work our files differently, however. Maybe without noticing it, we are pushing downwards, or lifting upwards as we file. Or we might have set our sharpening jig to hold the file too high or too low. The result, over several sharpenings, will be that the gullet will gradually change shape - if you tend to push down as you file, or the jig is set too low (not good), the gullet will take on a more pronounced shape, becoming deeper and rounder, as the file works its way under the cutter's top edge. You may also be filing into the chain links
, but that's something else! If you file with an upward pressure, or the jig is set too high, the gullet will become shallower, or less pronounced. Either way, one day you'll notice that your gullets are looking wrong and some work may be needed to get them back as they should be. If your gullet has become too shallow and you go at it with a smaller file to deepen it, you'll only be sharpening the side edge, not the top, because the file is narrower than the gullet. Or use a bigger file when the gullet has become too pronounced, you'll only be getting at the top edge, not the side.
So that's what happens if you use a file that's too big or too small. I'd say to stick with the recommended size and use an even pressure, working the file horizontally into the cutter. If you notice after time that the gullet shape is too much this or that, then stay with the right-sized file but change your jig setting up or down, or pay more attention to the way you file and gradually get your cutters back to the way they should be.
As some others here do, I switch to a slightly narrower file once my cutters have been filed back to near the witness mark - partly because the top cutting edge gradually reduces in height towards the back, but also the drive-link of the chain is higher than the tie-strap and I'd rather not be filing into it.
Personally, I'm aware that if I don't pay attention, I'll be working the file downwards, so consciously have to counter that with a bit of upward lift. I also seem to apply more pressure when filing one side of the chain than the other, so end up with two different gullet shapes on the one chain...