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This can probably answer your questions.

A key idea of land value taxes is it's on land value, rather than land area. Urban land is faaaaar more valuable than urban land on a per-acre basis, so someone who owns 1 acre of land in Manhattan will pay vastly more than a farmer who owns 1 acre in rural Nebraska.

As for appraisal, we already sorta do this with property taxes, as property taxes tax the land value + improvement value. With land value taxes, we simply seek to tax just the unimproved land value. Why? Property taxes can disincentivize development and incentivize land-hoarding and speculation. In contrast, even a milquetoast land value tax has been shown to reduce land speculation.