Learn Finnish: Onko pikalähetyksen toimitusaika lyhyempi meritse vai maitse? - Is the delivery time for express delivery shorter by sea or by land?

The prolative case ending -tse is almost always attached to the plural stem of a noun. The word for "land" is maa, and its plural stem is mai- (as seen in the plural inessive maissa). Therefore, adding -tse gives us maitse. Notice that meritse ("by sea") also uses the plural stem meri-, which just happens to look identical to the basic singular form meri.

Could I just use the adessive case, like laivalla (by ship) or merellä (at sea), instead of the prolative?

You can use words like laivalla or kuorma-autolla to specify the exact vehicle used. However, when talking broadly about the route or logistical medium, the prolative forms meritse (by sea), maitse (by land/overland), and ilmateitse (by air) are the standard, professional ways to express this in Finnish.

Why is the word for "or" vai here instead of tai?

This is a great refresher on asking questions! In a direct question where the listener is expected to pick exactly one of the specific options presented, you must use vai. Tai is used in statements, or in questions where the options are open-ended or not mutually exclusive. Since this question asks for a strict choice between sea and land, vai is required.