は does indeed mark new information, and は is also inherently contrastive. が can be used as a subject particle, when (as you point out) it is marking focus, but not necessarily always new information (because if it is contrasting or comparing, then は might be a better fit). When you have complex sentences with subordinate clauses the subject of the subordinate clause will take が, whereas the main topic will still be は. The difference between subject が and topic は is one of the TRICKIEST out there.
To get technical, verbs like わかります and ちがいます are intransitive verbs. Intransitive verbs, as you pointed out, are often understood in English by using the passive voice (being understood) - but they are not passive. Japanese has far more intransitive verbs than English and generally avoids the passive voice except in specific situations (adversive/honorific). Japanese also has many transitive/intransitive verb pairs: 終える (finish) and 終わる (end), for example. The difference between the transitive "finish" and the intransitive "end" is that "finish" requires agency (someone did it!) and "end" can just happen naturally. (The teacher finished class/ The class ended). Whether to use the transitive or intransitive is a long topic, but the intransitive is used more often when the focus is on what happened and not who.
Intransitive verbs take the particle が, transitive take を. In this sense they are both marking the object of the verb - 日本ごがわかります does not mean "Japanese understands." Even if we think of わかります as having a passive meaning "to be understood" (due to its intransitive nature), the "what" that is being understood is still "Japanese." Because が is marking the "what" (and not the "who") I think it is more suitable at this point to just think of it as an object marker (and not subject, which implies an agency it does not have).