For question 1), the exact number will vary depending on the elevation model you use for the calculation. High resolution elevation models are available for land, but for sea the resolution is much lower. The best global elevation model covering both land and seafloor is arguable ETOPO1, with a resolution of about 2 km. And if we mask all areas outside of the range -200 to 800 m it turns into this
And you can see that most tropical forest and large areas of boreal forest are included, so I wouldn't be surprised if 99% of living land species are within those ranges.
Now, the total area within those limits tuns out to be $1.286 \times 10^8 {km}^2$ of a total of $5.095 \times 10^8 {km}^2$ (A good match for the figure of $5.101 \times 10^8 {km}^2$ listed by wikipedia). Giving a total of 25.2% of Earth's surface.
From that total, a 5.3% is contributed by the terrain between -200 m and sea level ($0.270 \times 10^8 {km}^2$).
Note that so far we have NOT made any distinction between water covered and dry surface. Now, that distinction seem weird to me, as it rules out massive areas of shallow seas full of life. The oceans are know to contain 15% of the known species, therefore, ruling them out immediately render the "99% claim" invalid. Instead, that distinction seem to be there to include the minuscule amount of dry land between 0 and -200 m, that in turn is in general very dry (otherwise they would become lakes) something that doesn't makes any sense to me. If the sentence you heard really refers to "dry land", I would think it must then refer to land species only. Anyway, it is not difficult to properly answer question 1 by quantify the relevance of those below-sea-level dry areas. That can be accomplished using the MODIS global water mask, a very useful dataset at 250m resolution that allows to distinguish between dry land and water covered areas. It looks like this:
(It doesn't cover Antarctica, but that continent doesn't contain any below sea level interior lands as seen in the first figure, so it doesn't really matter)
Using the two datasets, I've calculated that the surface of dry land between 0 and -200 m of elevation correspond to $0.0065 \times 10^8 {km}^2$ (a 0.1% of Earth's surface).
Taking that into account, the percentage of dry land between -200 and 800 m is a 69.1% of Earth's dry surface, or a 20.1% of the total Earth's surface.
For question 2, I think your proposed interpretation is valid, and reasonable. But also other interpretations (like the total biomass mentioned in the comments) are valid. Nevertheless, as mentioned above it must refer to that "99% of land species live in dry land between -200 and 800 m" or that "99% of all species live between -200 and 800 m". Otherwise the claim is incompatible with the above mentioned fact that 15% of species live on the oceans.
A second caviat is that a large amount of species are yet to be discovered, perhaps up to the 86% of them, and those will arguably be found preferentially in the less explored areas of the oceans.
I haven't seen quantitative biodiversity maps considering estimated for all known species. You will be able to validate that claim if you consider one special well studied group, like vertebrates or vascular plants. Tor those two groups, comparing the following two figures with the top one makes the "99% claim" perhaps reasonable, but an overwhelming majority of species don't belong to those groups, and I don't know if the biodiversity distribution would be similar.
(vertebrates biodiversity map from savingspecies.org)
(vascular plants biodiversity map from Hamburg University)
If an actual number wants to be calculated based on actual data, the GIS datasets at biodiversitymapping.org are a great resource.
Perhaps one argument in favour of the biomass interpretation of the claim, is that it would be a much easier and better constraint calculation.
