Is there a source for why many people (Ashkenazim) use a knife to pre-mark the challah where they will cut it before making the bracha on Shabbos?
The source for cutting into the bread before making the blessing is in order to minimize the appearance of interruption between the blessing and the eating (S.A. O.C. 167:1 with Magen Avrohom 3). This cut should be made such that it is not deep enough that were you to lift the smaller part the larger part would not come up with it (ibid). However, that is only for actually cutting into the bread. When the bread is cut this way, there is a concern that one may come to cut too deeply and separate the bread such that it is no longer one piece of bread. That being the case, on Shabbos when there is an additional concern of Lechem Mishna, we'd rather not risk it, and therefore it is best to not do so on Shabbos (Rema ibid with Magen Avrohom 5). The Kaf HaChaim (167:7) implies from the Rosh that with soft or thin bread, there is no need to make any slice into the bread.
What you may have seen done is actually not really cutting into the bread. We (I include myself among those who have this practice) merely make a mark, as you indicated in your question. The source for making the mark is the Magen Avrohom (O.C. 274:1, citing the Bach citing the Maharshal). One supercommentary there suggests the reason for the mark is still based on minimizing the interruption (Levushei S'rad to Magen Avrohom 274:1). Another (Machazis Hashekel to Magen Avraham 274:1, s.v. המדקדקים) says the concern is to avoid the interruption of finding a place to cut and measuring off the correct sized piece of bread after the blessing. While this may seem like a negligible amount of time, I suggest that the concern is based on that which the Shulchan Aruch (O.C. 167:1, 274:2) writes, that on weekdays you should not cut off a piece larger than a kezayis because it is gluttenous. The Rema, as explained by Magen Avrohom 6, writes that you need to give a kazayis of bread from the piece which you cut off to each person at the meal. Therefore, you need to make sure that the piece you are cutting off is big enough to divvy up from it a kazayis sized piece to all present, but on weekdays not larger than that. Therefore, for those who follow this opinion, it is quite reasonable that this measuring, if done after the blessing, could take several seconds of estimation, and therefore is better to be done (and marked) before the blessing.
We want to minimize the interruption between reciting HaMotzi and eating the bread, but we also want to recite the berachah upon a whole loaf, if possible, to show respect for the berachah. So when do we actually cut the bread?
Early sources ... felt that cutting the bread does not constitute a significant interruption. Others agree, particularly with thin-crusted bread like ours. Nonetheless, some suggest one should satisfy the “interruption” concern by starting to cut the bread - without cutting too deeply - before reciting HaMotzi.
To summarize his conclusion: The Shulchan Aruch Orach Chaim 167:1 discusses this. Many, many sources write that on Shabbos, it's actually better to not "pre-score" the bread. However, in the yeshiva world it's taught to always pre-score the bread, probably for consistency throughout the week.
I have heard that it is because the bread is supposed to be ready to eat, but at the same time, hamotzi should be made on a whole loaf. The compromise is to make a small slice, so that it's "cut", but still whole.
Going to try and find sources soon.
It would seem this is based in the Shulchan Aruch 167:1. The general rule is that one should prefer to make a blessing over a complete object to give honor to the blessing. Additionally, one should minimize interruptions between the blessing and eating. As a compromise, when breaking bread one can cut into the bread up until the point where if you lift up the slice, the rest of the loaf comes along. At this point, it is still considered "whole" for the blessing, and you have minimized the time spent cutting after the blessing. On Shabbat however, where we need Lechem Mishneh (2 whole loaves) we are careful to not cut at all before the blessing (lest the bread break and we lose our Lechem Mishneh -- see Tosfot infra), even though it means a longer wait between the blessing and eating.
Here is the Shulchan Aruch inside:
וצריך לחתוך מעט, שאם יאחוז בפרוסה יעלה שאר ככר עמו, שאל"כ חשוב כפרוסה, ויניחנה מחוברת לפת ויתחיל לברך ואחר שסיים הברכה יפרידנה, כדי שתכלה הברכה בעוד שהפת שלם... הגה: ובשבת לא יחתוך בככר עד אחר הברכה, כדי שיהיו הככרות שלימות ומ"מ אם שכח וחתך כמו בחול, אינו מזיק
(See also Brachot 39b and Tosfot there sv Vehilcheta.)
The Arukh HaShulchan (167:5) notes that the widespread custom which should not be changed was to not cut the bread "at all" before the blessing on Shabbat, even though it is done during the week.
Everyone seems to agree that if you did cut the bread early on Shabbat as well that Bedieved it's ok.