"There are those whom understand this sentence, and those who do not"
This is not correct, it should be:
"There are those who understand this sentence, and those who do not"
It should be "there are those who understand this sentence" for the same reason it should be "and those who do not". Why would you expect the relativisers to be different when the structure of the relative clauses is the same?
It should be "there are those who understand this sentence" because "who" is the subject of the relative clause, i.e.: they understand this sentence. If, for some bizarre reason, you wanted to rephrase it as "there are those by whom this sentence is understood" then you would use "whom" because "whom" goes with the preposition "by", i.e. "this sentence is understood by them".
A nice trick you can use is to try playing with the numbers and see what happens to the verb. Let me show you what I mean. Instead of "there are those who understand this sentence" try "there is a man who understands this sentence". Notice that it has become "understands" to agree with "a man" (which is what "who" refers to, we say it is the "antecedent" of "who"). Thus "who" is the subject of "understands". Whereas, in "there is a man by whom these sentences are understood" the verb agrees with "these sentences", it's plural ("are understood", not "is understood"). Thus "these sentences" is the subject of the verb, not "whom" because "whom" refers to "a man", which is singular and the verb is not singular.
You can try and avoid using "whom" altogether if you want, but it remains part of the language, and if you try and avoid it completely you'll find yourself saying "to who it may concern" and "with who?" Better advice would be not to overthink and use "whom" only where you know it belongs.