Learn Arabic (Modern Standard): لن يشرب الخمر أبدا.

Because the sentence is talking about the future. The word أبدا is used for future absolute negation, which we know applies here due to the future negative particle لن. If the sentence were about the past, you would use قط instead.

Why does the verb يشرب take the subjunctive mood here?

The negative future particle لن always forces the present tense verb that follows it into the subjunctive state (mansub). For a regular verb like يشرب, this changes its default final damma to a fatha, making it يشربَ.

Why does the word أبدا end with a tanwin fatha (-an)?

It functions as an adverb of time, which in Arabic grammar is called a tharf zamaan. Adverbs of time and place must take the accusative case (mansub), which is marked here by the tanwin fatha.

Does الخمر refer specifically to wine or to alcohol in general?

While historically it referred specifically to fermented grape wine, in Modern Standard Arabic الخمر is used as an umbrella term for any alcoholic beverage or liquor. Because it is the direct object of the verb, it also takes the accusative case, becoming الخمرَ.