"...land that loses ice weighing it down rises."

Correct. Eustatic, it is called, rise or lowering of land due to the mass of ice accumulating or declining, affects not only regions with fluctuating ice masses, but also regions in the general area, which may settle lower when other areas rise, or rise when other areas lower, as well.

"...ice, sitting on the oceans makes the ocean rise."

Ice shelves that have always floated on the sea do not raise sea level when calving ice bergs. Ice bergs calving off an ice shelf have always been affecting sea level and do not create additional volume of ocean water when they separate from the ice shelf.

Ice that was supported by land and falls into the sea, such as where a glacier flows downstream to eventually reach sea level, does create isostatic, it is called, rise of sea level. In fact, increasing depth of water over the sea floor can cause the sea floor to lower, by increasing the mass of water pressing down on it, and this can cause nearby land to rise. There are some surprises that occur, because we do not well understand the distribution of pressure from isostatic and eustatic movement and how it can produce pressure elsewhere that causes eustasy and isostasy.

If you blow up a bunch of balloons and put them in a cardboard box until they begin to protrude up out of the box, and then try to put a lid on the box, pressing down on the lid will cause the sides of the box to bulge as the downward pressure of the lid is transferred from balloon to balloon, eventually to increase the pressure against the sides of the box. With a carton, we know the corners are stronger, so the bulging will all occur at the flat sides of the box.

The Earth, however, has no corners, and the materials in it aren't all the same density or fluidity. We do not well understand such differences below the surface of the Earth, making the interplay of eustasy and isostasy difficult to understand and predict.

However, the water cycle is temporally interrupted by water being locked up in ice, whether on land or on the sea. Frozen water doesn't cycle until it thaws. As water is removed from the cycle of evaporation and precipitation by being locked into ice shelves or glaciers, precipitation refilling the ocean does not equal evaporation emptying the ocean, and sea level is eventually lowered by a significant amount, more than 100 meters during the LGM (late glacial maximum), in an ice age.

The interaction of such isostasy and eustasy isn't always regular and predictable, so not all land currently at the shore was more than 100 meters above sea level during the LGM. There are places along the Canadian western shore that were shore then, in fact, due to eustatic rebound as the Cordilleran Glacier melted after the end of the last ice age equaling the isostatic rise in sea level in those locations.

One of the best publicly available resources for finding out more regarding how the end of the last ice age geologically affected Earth, and a discussion of isostasy and eustasy, can be found at Randall Carlson's site Kosmographia, in the dozens of videos he has published of discussions resulting from his field trips and others work. I have been amazed at the incredible megafloods that resulted from glacial meltwater pooling in enormous lakes as the climate warmed and then those lakes suddenly emptying, dozens of times over several thousand years, Randall and his guests reveal.

Thanks!

Edit:

"...glacier ice falling (a particular kind of snow)..."

Every kind of snow, that accumulates when it doesn't melt, becomes a glacier where it accumulates. Eventually the softest snow becomes so compressed by the weight of snow on top of it that it become rock hard ice.