No and no:

1. No, 5e does not use the Great Wheel cosmology — not by default. It's one of the many options available for a DM, but 5e presents only ingredients for a homebrewed cosmology, and very few pieces that are assumed as defaults (usually in things like magic item descriptions, such as the bag of holding).

2. In the Great Wheel cosmology, the Astral is entirely separate from the Prime Material. It is only accessible via magic, either more powerful magic that directly moves one to/from it, or via smaller magic that can get you into the Ethereal, through which you can travel to get near its border with the Astral and then use other magic or portals to hop from it to the Astral.

   This means that a Githyanki ship can't raid outside the Astral without very powerful magic that can essentially Gate the entire thing; and even then, an Astral ship only works in the Astral Sea anyway, and would need entirely different magic to operate in a Material atmosphere/space/crystal sphere/whatever arrangement that particular world in the Prime has.

Basically, the planes are physically separate and can't be traversed by mundane means. There are some exceptions (such as the borders between the Outlands and the Outer Planes, but even that's complicated, since how the “border” works between those infinite planes is quite strange in practice), but as a rule: no, you can't just walk, fly, sail, crawl, or trebuchet between the planes.

No and no:

1. No, 5e does not use the Great Wheel cosmology — not by default. It's one of the many options available for a DM, but 5e presents only ingredients for a homebrewed cosmology, and very few pieces that are assumed as defaults (usually in things like magic item descriptions, such as the bag of holding).

2. In the Great Wheel cosmology, the Astral is entirely separate from the Prime Material. It is only accessible via magic, either more powerful magic that directly moves one to/from it, or via smaller magic that can get you into the Ethereal, through which you can travel to get near its border with the Astral and then use other magic or portals to hop from it to the Astral.

   This means that, no, a Githyanki ship can't raid outside the Astral without very powerful magic that can essentially Gate the entire thing. Even then, an Astral ship only works in the Astral Sea anyway, and would need entirely different magic to operate in a Material atmosphere/space/crystal sphere/whatever arrangement that particular world in the Prime has.

Basically, the planes are physically separate and can't be traversed by mundane means. There are some exceptions (such as the borders between the Outlands and the Outer Planes, but even that's complicated, since how the “border” works between those infinite planes is quite strange in practice), but as a rule: no, you can't just walk, fly, sail, crawl, or trebuchet between the planes.

On the plus side, this means that you don't have to figure out why Githyanki don't constantly raid the Forgotten Realms or somesuch.

But on a completely different plus side, the lack of a default cosmology means you can trivially say that the Planes are contiguously connected in a useful way to allow Githyanki raiders to bother the Realms, if that is the campaign you wish to construct!