4th position on a Bb would be C *minor* (strictly: the C dorian scale, which has a minor 3rd), so you’re not gonna be able to play C major melodies that way.
With the other issue, I’m guessing you’re referring to the fact that 10th button pull note is LOWER than the 9th button push (and pull) note – I did a double take over that too when I first tried one of these things. But the pattern is totally consistent: push notes go do-mi-sol, and pull notes go re-fa-la-ti. Since there are three push notes but FOUR pull notes, the pushes and pulls are gonna get more and more out of sync with every higher octave; no way around that without changing the whole setup pretty drastically. There’s just no way to evenly divide 7 (# of notes) by 2 (# of bellows directions). If you kept adding higher buttons, image how unintuitive it would get by buttons 12, 13, and 14.
(The one exception to the pattern is the 1rst button pull, which ought to be a low fa – I think they change it to sol so you can play a useful chord using the bottom three buttons together. I know they break the pattern on the lowest holes of a harmonica for the same reason.)
Setting aside issues already discussed re the relevance of "positions" and the numbering thereof, the answer to your first question is yes -- C is the second note in the Bb scale, so assuming 4th position is built around the 2-note, 4th position on a Bb accordion would be key of C. Keep in mind that playing in C on a Bb box, you don't have access to either the 3rd note (E) or the 7th note (B) in the C scale.
As to your second question, builders or historians may be able to provide a "correct" answer. Practically speaking (and assuming by "top button" you mean the 1 button), it seems to me at least that continuing the "pattern" down to the 1 button doesn't provide much benefit (since not a lot of melody is going to be played at such a low pitch), whereas breaking the pattern provides some nice capabilities that wouldn't otherwise be available. Specifically (and speaking in terms of a C accordion):
1. The G note on the 1 pull allows you to end songs in the key of G (of which there are many) with a nice full G chord (1-2-3 pull) that actually contains a G note.
2. I've heard at least one player (Chris Miller) doing a traditional bass shuffle in G that relies on that low G note (1-3 pull / 2-4 push / 1-4 pull / 2-4 push, etc.). It's a cool sound that couldn't really be done without the low G on the pull.
Nathan - Yeah, anyone trained on pretty much any instrument except Cajun accordion thinks of "high" and "low" in terms of pitch. Despite that fact (and despite the conventional numbering of buttons on a Cajun accordion), the majority of Cajun accordionists I've played with tend to speak of "high" and "low" (or "top" and "bottom") buttons in terms of altitude / distance from the ground rather than pitch. Hence, I assumed Greazy's reference to the top button meant the 1 rather than the 10 (also because, as you point out, the 1 pull is the only real deviation from the "pattern"). Very confusing, but what can you do?