The short answer is that OliverBM's assumption seems to be correct and DLC characters are not counted towards these milestone achievements. I would've preferred more authoritative sources, but posted user experiences was the best I could do for most of them.
According to IGN, the Arcade Champion achievement does not include the DLC characters, but does include the unlockable characters:
Tag Ladder does count: You get this achievement when you beat the standard or tag ladder with each of the non-DLC 27 characters (28 on the PS3 version). You can use as many continues as you wish, and you can do this on any difficulty level.
According to this answer, Finish What You Start! does not include DLC characters, but note from reading elsewhere that it does include the unlockable characters:
And no, DLC characters dont count towards the trophy.
According to this thread on xbox360achievements.org, My Kung Fu Is Stronger does not include the DLC characters, but does include the unlockable characters:
-#112, just to be absolutely clear, even if I have the DLC characters, it only counts towards the originals?
-that is correct
According to this post, e-X-cellent!, The Grappler, and Ultimate Humiliation do not include the DLC characters**, but from reading elsewhere do include the unlockable characters:
It seems that DLC characters are not needed for trophies, I got milestone trophies (Finish What You Start !, Ultimate Humiliation, The Grappler, e-X-cellent...) without playing with Rain, Kenshi, Skarlet and Freddy.
Contrary to the current accepted answer, it appears that you do not need to listen to dialogue for a minimum of 8 seconds. I tested this today and made a quick video of my results, see it here.
In summary, you can quickly skip through all of the dialogue and still get credit toward the achievements.
Edit: I have run more tests, here is a link to a Youtube video where I skip through 18 conversations of varying lengths at full speed and get credit for all of them. It's not exactly a riveting video, but I think that it sufficiently supports my answer. Here is the video (the footage is sped up to make the video shorter).
Best Answer
The specific achievement you mention is obtainable as there are actually 10 character slots. You can also get this achievement by creating, leveling, then deleting characters (or selling them, after Blizzard allows characters to be sold on the AH).
Regarding the rest, it is indeed possible to get all achievements; none of them should be mutually exclusive.
In fact, here is a thread where a number of people discuss their attempts to get the "world first" for obtaining all achievements.
The exception is that, as @aolszowka mentions, some Feats of Strength are no longer obtainable. However, these are usually excluded from "all achievements," and in fact this is one of the reason Blizzard invented feats of strength.