I would like to know whether Sea Level Rise is linked to Greenhouse Gas emissions and what the mechanisms are behind it.
Melting glaciers are more difficult to show a direct relation. By this source there are over 130,000 glaciers in the world, and while there is a fair bit of overlap, to properly show a causal relation, you'd need to look at individual glaciers to determine the cause. You wouldn't need to look at all 130,000, but you'd need a solid sampling to demonstrate a causal relation.
What's more, under the right conditions, glaciers can grow larger as the local weather grows warmer. Warmer weather can lead to increased snowfall, which can enable glaciers to grow, even in a warmer climate. Article on that here.
The two simplest ways to make this argument is looking at the percentage of glaciers that are melting or to look at total ice volume in those glaciers. (For the 2nd one, I'd ignore the continental ice sheets and just look at the smaller glaciers), but it can be done either way.
By this article, about 90% of glaciers are shrinking world wide. If climate wasn't changing, I'd expect that to be closer to 50%. Even when climate is changing, for example, when ice ages stop are start, those are usually driven by the Northern Hemisphere having colder summers (begins the ice age) or the Northern Hemisphere having warmer summers (ends the ice age), with the Southern Hemisphere behaving in the opposite way. That suggests to me that even during the rise or fall of ice ages, 90% of the glaciers moving in the same direction probably doesn't happen. 90% of glaciers losing ice appears to be strong evidence of being caused by climate change, but that ratio lacks statistical teeth because there's no historical data to show that 90% of the world's glaciers losing ice is unusual. It seems unusual, but it's difficult to prove.
The other avenue would be to look at the total amount of loss of ice in the world's glaciers. See page below. I didn't see a number listed anywhere, but a quick calculation, Earth's glaciers are losing on average about 60 cubic miles of ice in an average year. That's pretty significant ice loss.
cdn.antarcticglaciers.org/wp-content/uploads/2014/11/images_Assessment-Reports_AR5-WG1_Chapter-04_Fig4-25_errata.jpg
from source
But both these arguments have the same weakness. Both seem to be very good evidence, neither shows a causal relation. The only way to do it scientifically would be to go through a large enough sample size of glaciers and show a pattern of causality. At least, I don't see any other way to show a direct relation.
That said, saying "90% of the worlds glaciers are losing ice" is a pretty good argument, as is saying that Earth's glaciers lose about 60 cubic miles of ice in an average year.
Not all the earth's ocean's are at 10 C, but using this as an estimator, the $1.35 \times10^9 \text{ km}^3$ will increase by $1.31 \times10^6 \text{ km}^3$ with a 1 C increase in temperature. If you divide that by the surface area of the ocean, 510 million $\text{ km}^2$, you get an approximately 2.5 meter increase in sea level.
That calculation is not at all rigorous; deep ocean water is colder than 10 C and at lower temperatures thermal expansion is much less (just look at the linked chart to see), but it does demonstrate that there will be a detectable rise in sea level from thermal expansion of seawater as the planet heats up.
Basically, the claim is that CO2 makes the earth warmer by insulating the earth and preventing the escape of long-wave radiation, and this higher average temperature causes glaciers to melt and the sea level to rise due to the addition of meltwater.
(The argument is not heard too often these days because of the historical problem. In Roman times (1800-2300 years ago) sea levels were substantially lower than they are today, yet the earth's climate was warmer than the modern climate. For example, in Roman times Britain grew grapes commercially and was a big wine exporter, but now that is no longer possible because the climate of Britain is too cold to grow grapes. So, as a consequence of this problem, the sea level thing is not touted as much as it used to be back in the 1980s before the contradiction was noticed.)