"That chair is low."
You don't need to use です if the sentence ends with a i-adjective. Those inherently have a tense (e.g. present/past) and the auxiliary verb "to be". E.g. ひくい, by itself, already means "it is low" (instead of "low" only, like English adjectives). It is more polite to add です though.
Except that in this case we have an adjective which conjugates like a verb so you can omit the です in any case. Well except when you need to be extra polite.
What you said is correct for sentences that don't have any verb at all, not even a conjugating, verb-like adjective.
あの, その, この must all modify nouns ie. they cannot be used on their lonesome. あの means that (whatever it is modifying) over there - far away from both the speaker and listener. その means that (noun) there - closer to the listener. この means this (noun) here - closer to the speaker
は marks the topic of the conversation, it translates roughly to "regarding the...". It also marks the noun as the one doing the verb.
So you can interpret this as "Regarding that chair, it is low."
And yes, using が would be wrong here, the chair all by itself is doing the verb, is being low, so you don't need to mark anything else with が in this case.
To further explain EduardAlex13's reply: transitive verbs are done by one thing to the other; 「カースクナックさんは いすが あげります。」 = "kaasknak lifts the chair". Please note that カースクナックさん (kaasknak) is marked with a は as the one doing the verb, while いす (chair) is marked with が as the thing helping with the verb or receiving the verb.
On the other hand,「いすが あがります。」 = "The chair rises."... All by its own! The chair is receiving the verb “to rise” but nothing is doing that to it, so nothing is marked with a は.
In case you haven't noticed the verbs: あげります (note the second character: げ!!) means "to lift something", the は-noun lifts the が-noun; it transcends from one to another and is thus called a transitive verb.
While あがります (second char again, が!!) means "to rise". Here the が-noun rises by itself, it doesn't need a は to do it to them; it doesn't transcend and is thus intransitive.
Sorry for the brain-boiling explanation, though, but I hope it helps!