Eruvin 44b - Shavas b'm'arah

I had several questions on the case of the person who began Shabbos in a cave, daf מד amud beis.

(a) In the gemara's case, where the roof of the cave is less than 4000 amos from one entrance to the other, the gemara says that one needs the principle of "havla'as techumin" in order to allow walking across the whole roof from one end to the other. In other words, if we didn't hold by havla'as techumin, if one walked out the south entrance and walked 2000 amos north on the roof, he would be required to reenter the cave and go out the north entrance to continue on the roof (Rashi) - even though when he had gone 2000 amos from the south entrance, he was already standing in the (overlapping) techum from the north entrance. Why is that? What does it have to do with "havla'as techumin"; why isn't it sufficient that he is now actually standing inside the techum from the north entrance? He is still within 2000 amos of the place where he began Shabbos.

"l'saber es ha-ozen", imagine a person walking west out of a city 1000 amos, turning north, circling the city at a distance of 1000 amos, and coming to the eastern side of the city 1000 amos distant. Would anyone say that he has taken advantage of "combining the east and west techumin"? Or would we say, I don't know what you're talking about; he never went more than 1000 amos from the city, so he is of course still inside the techum. He is within 1000 amos of the city; what more is there to say?
I know that this argument is wrong, but I don't know why.

(b) Why does the gemara give a case where the base of the cave is
4000 amos (and it slants in at the top)? That seems to have nothing to do with it. Would it matter if the cave bottom was 5000, 4000, or 3000 - as long as the top is the same = just less than 4000? If the size of the base is irrelevant, why does the gemara mention it?

(c) Is this cave case brought by the poskim (I didn't see anything marked in the gemara), and if not why not? It seems to be the halacha, and apparently not all that obvious.

Follow-up question on the same gemara: Rashi says that the techum is measured 2000 amos in each direction, from each of the two openings at the top of the cave. It is clear then that Rashi considers the entire cave to be his makom shevisah, not just the center of the cave. (Otherwise, he would not have 2000 amos from each of the openings, but only what's left after measuring from his place.)

But why is that? The halacha is that we only give a person an entire enclosed area, if the area was מוקף לדירה (but a cave is presumably not מוקף לדירה) or if the area is less than בית סאתים, five thousand square amos. In this case, the cave (which is 4000 amos in length), would have to be very thin, < 1.25 amos wide. And no one mentions that. Does the cave need to be man-made?

Update: Now I see daf 61b, where the gemara compares a stam mention of a cave in a mishnah to the cave of King Tzidkiyahu - and it's clear in the gemara that both are assumed to be man-made (and מוקף לדירה).

I don't know if this is helpful, but I thought I should post what I think is a companion case. That's from 55a, עיר העשויה כקשת - a city shaped like a bow. The question in the gemara is, do you consider the interior of the bow (the יתר, the "string") to be part of the city interior, so that you measure the 2000 amos from there as well. It depends on a number of factors: Are the two ends of the bow less than 4000 amos apart, so that "their techumim combine (הבלעת תחומין)" (Rashi), and are you less than 2000 amos from the midpoint of the bow when you get to the string.
One point made in the gemara by Abaye (55b) is that the fact that you can walk from one end of the bow to the other, via the midpoint, makes it more likely that the techumin should be combined. This is maybe similar to the idea that you can always walk from one entrance to the other, inside the cave.

Still not too clear on any of this, but I thought this case ought to be added into the picture.

Is it obvious that this din would not apply to a city? That is, if a city is surrounded by a wall, with only gates at the east and west, people still have 2000 amos in every direction from the wall. We would not say that their techum extends only from the two gates, and the only way a person can walk all the way around the city is if it's less than 4000 amos from one gate around to the other. I think that's true - the poskim I've seen discussing the techum of a city never seem to mention that the regular dinim only apply if the city has no wall, or gates on all four sides!

So part of the din of the cave must come from the way the roof is "away" from the cave. The Rashba discusses it in terms of מחיצות שאינן ניכרות: the walls are not perceptible to those standing on the surface, so the surface is not considered part of the cave.