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I am looking for the names of these three short stories that I read long back in an anthology of sci-fi stories.

First Story: It's about a planet mostly water that has been seeded by some intelligent space traveling species. And the new inhabitants of the planet lives in a narrow part of the large ocean that the planet is covered with. And these creatures although intelligent are very small so that it is impossible to break the surface tension of the water for them. And among these creatures there is an individual who wants to break the surface tension and see the "stars". ( so clearly influenced by "nightfall" )

Second Story: It is about a planet in which there is a wall which the locals call the end of the planet. And an individual will try to cross the wall only to find that it is wrapped back to the point where the wall begins.

Third Story: It is about a planet which has a small and fast moon that orbits too close to its surface.

It could be that all these are from the same anthology, it will be great if one can point out the anthology. I would like to read these again.

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The first story is "Surface Tension" (see also the Wikipedia page) by James Blish, part of his Pantropy series, collected in a fix-up novel called The Seedling Stars. "Surface Tension" was first published in Galaxy Science Fiction, August 1952, available at the Internet Archive; click here for download options. (The story was also the subject of this old question.)

Silently, Lavon pointed, his heart pounding.

The entire dome of indigo above them was spangled with tiny, incredibly brilliant lights. There were hundreds of them, and more and more were becoming visible as the darkness deepened. And far away, over the ultimate edge of the rocks, was a dim red globe, crescented with ghostly silver. Near the zenith was another such body, much smaller, and silvered all over . . .

Under the two moons of Hydrot, and under the eternal stars, the two-inch wooden spaceship and its microscopic cargo toiled down the slope toward the drying little rivulet.

The second story is "The Wall of Darkness" aka "Wall of Darkness" by Arthur C. Clarke; first published in Super Science Stories, July 1949, available at the Internet Archive; click here for download options. (The story was also the subject of this old question.)

Shervane ran his eye up the long flight of steps on which no feet would ever tread again. He felt few regrets: he had striven, and no one could have done more. Such victory as was possible had been his.

Slowly he raised his hand and gave the signal. The Wall swallowed the explosion as it had absorbed all other sounds, but the unhurried grace with which the long tiers of masonry curtsied and fell was something he would remember all his life. For a moment he had a sudden, inexpressibly poignant vision of another stairway, watched by another Shervane, falling in identical ruins on the far side of the Wall.

But that, he realized, was a foolish thought: for none knew better than he that the Wall possessed no other side.

The third story is "The Holes Around Mars" by Jerome Bixby, first published in Galaxy Science Fiction, January 1954, available at the Internet Archive; click here for download options. The story is also available as a Project Gutenberg etext.

That night in the ship, while we all sat around, still shaking our heads every once in a while, Allenby talked with Earth. He sat there, wearing the headphones, trying to make himself understood above the god-awful static.

". . . an exceedingly small body," he repeated wearily to his unbelieving audience, "about four inches in diameter. It travels at a mean distance of four feet above the surface of the planet, at a velocity yet to be calculated. Its unique nature results in many hitherto unobserved—I might even say unimagined—phenomena." He stared blankly in front of him for a moment, then delivered the understatement of his life. "The discovery may necessitate a reexamination of many of our basic postulates in the physical sciences."

[. . . .]

"Inasmuch as Mars's outermost moon is called Deimos, and the next Phobos," he said, "I think I shall name the third moon of Mars—Bottomos."

Anthology? There is no anthology containing all three of those stories in the Internet Speculative Fiction Database. Two of the stories, "Surface Tension" and "The Holes Around Mars", are in the anthology Where Do We Go from Here? edited by Isaac Asimov.

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    This was an all-time great answer--to any question--ever. – witttness Jul 27 '15 at 2:13
  • I agree @witttness. – mukhujje Jul 27 '15 at 5:58
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    I consider Walls of Darkness to be one of the most mind-bending stories I read as a kid. – Maury Markowitz Oct 21 '16 at 17:23

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