Bereishis Rabbah (55:8-9) describes how Avraham, who had exerted so much effort into doing the will of Hashem to offer Yitzchak as a karban, felt bad that he wouldn't be able to do so. Thus, when he saw a ram that just happened to be sitting there, he grabbed the opportunity to "make up" for it, and he shechted it in place of Yitzchak. The Midrash describes this ram as a "Temurah" for Yitzchak. (Note that, obviously, Hashem didn't actually want Yitzchak shechted. This Midrash is to emphasize Avraham's will, not Hashem's.) It seems that the Midrash is explicitly emphasizing the fact that the passuk refers to this ram as being offered "instead of his son."
With this Midrash I believe it's possible to answer all of your questions.
- In general, what exactly was the nature of this symbolic sacrifice?
To make up for the fact that Avraham wasn't able to shecht Yitzchak.
- Rashi tells us that with every action involved with the slaughtering of the ram, Avraham prayed that Hashem should consider their actions to have been done to Yitzchok. Did this actually change anything in the historic nature of this event? What if he hadn't slaughtered it, or had slaughter it but hadn't prayed?
Once again, Avraham wanted the ram to be a pseudo-Yiztchak. It just shows the great lengths to which Avraham wanted to fulfill this test. Avraham was so devoted to Hashem that even though he wasn't able to shecht Yitzchak, he still wanted to shecht him. Thus, he brought a ram in his place, and he davened that the ram should be treated by Hashem as well as being in Yitzchak's place.
- The special nature of this ram was exemplified by, possibly, making it to the list of items created at twilight, in the fifth chapter of Avos. ... I was wondering in general, what was so special about this ram and its slaughtering that it needed to be prepared at that point in time?
The Maharal (beginning of his piece on this Mishnah) quotes a Rambam who writes that Hashem "made a condition" with nature that, at certain points in time to be decided later, it should be altered for a neis to occur. Thus, he interprets the Mishnah as saying that Hashem made a condition with the land that in the days of Korach it should swallow his camp, and that shortly after Krias Yam Suf, when the Bnei Yisrael would need water, Hashem made a condition with the rock that it should give forth water, etc. Likewise, Hashem made a condition with this ram that it should be there in the zechus of Avraham Avinu, who would otherwise have been suffering from not being able to fulfill Hashem's will.
Now, this entire p'shat still begs the obvious question: as the Midrash (same source) attests to, Hashem's will was never that Yitzchak should be shechted, but that he should be placed on the Mizbeiach. Thus, why did Avraham need anything to take the place of Yitzchak? To that I do not have an answer, but I still believe that this p'shat is firmly rooted in a Midrash that clearly answers all of your questions.