Why do these verbs exist?
Tough historical/philosophical question. I'm going to leave it aside. :)
Are there any rules to determine if a verb uses が instead of を in this way?
Yes there are such rules.
One of the biggest separations is whether the verb is transitive (他動詞) or intransitive (自動詞). Using を to mark the object of an action is a major characteristic of transitive verbs. わかる and ある are both intransitive, so that gives you a strong hint that を is not the right choice.
Beyond that, you can categorize verbs based on how they use が to mark various pieces of complementary information (see link at end of post.) For example, verbs of existence, verbs of state, verbs of transformation...
In the most general scenario, you just have to memorize what particles are used by what verb to add some given information to it.
why do verbs like わかる require having a subject to mark with が instead of having a direct object to mark with を?
I basically answered this question in my last paragraph, but I want to note that が arguably does not mark the subject of わかる here. For example, let's revisit your example sentence:
In this sentence, who is the person who does not understand? It's the speaker. So the speaker is the subject (or perhaps the "topic"), not "ここ". In this case, "ここ" is the object of the verb.
Here is a table you can consult for more details: