The Japanese definition of ある is 人、物が存在する. Operative word is 存在 which means existence. So it doesn't really need a ている to express 継続的な状態. That's built in.
居る falls in the same camp. Not all verb conjugation makes sense for all verbs. Always exceptions.
This kinda also makes 存在する and 存在している mean pretty much the same thing now I think about it except I guess the latter is present tense only while the former can be future tense. You can't make such distinction with ある.
Pretty much every utterance falls into one of the following broad categories:
4. State (condition)
It can sometimes help when you get stuck if you try to figure out which of the four listed communicative purposes is involved.
Broadly speaking again, even if the constructions used vary between languages when translating something, you will usually find that it is the same communities purpose being fulfilled.....expressing either existence, action, possession, or state.
Both ある 持つ can mean 所有. In your example though ある is better to ask whether beer is available in a store. The latter sounds like you are asking if one is in possession of a beer. Really emphasizing the possession bit. 所持. But hey they could mean the same thing.
This is pretty unique to Japanese that 所有 can be expressed with 有る and 持つ.
In Chinese you can bang the 2 characters together but when translating into Japanese you are no closer to the answer.