彼ら is definitely gender neutral and 彼女ら can only have females in the group, right?
If you think using he in English when the gender is unknown is politically incorrect, then you would still want to worry about 彼ら a bit, too. You don't have to be too strict, but avoiding gender-neutral 彼ら when possible is a good habit.
And I think the singular 彼 strongly indicates the male gender, perhaps even more strongly than English he.
Adding -ら allows for a more precise statement. But I wonder, do they sound impolite and rough and would not be used in newspapers?
彼ら and 彼女ら are used both in formal and casual situations. There's nothing impolite.
Is 彼ら rarely used in speaking? And never in writing?
Is 彼女ら just never used?
They are used both in casual speaking and writing, but not as frequently as he/she/they is used in English. Repeating the original noun (e.g. 学生たち, その人たち, 山田さんたち), or simply omitting such pronouns, is the preferred way in Japanese.
Is あいつら not uncommon, but used in extremely informal conversations?
あいつら (as well as こいつら, そいつら) is more than just informal; it's rough, and frequently (not always) used in derogatory sentences. I would never use あいつ(ら) unless I'm really upset.
You cannot substitute たち for ら and say 彼たち, 彼女たち, or あいつたち, right?
彼ら, 彼女ら and 彼女たち are all commonly used, but 彼たち is extremely uncommon for some reason. I don't know why. But you can check this article.