What's the best way to do this?

You can assign a species name then give them male/female names and features.

Although they are simian humanoids, you can all them the Tribals or something. A tribe is a collective noun for humans, baboons, monkeys, and so forth. Assign gender-specific names after, like Simi (male).

I wouldn't call them men or women, even though they are humanoid. They are not human.

Depends on how deep you want to dive into culture.

Beware of "smeerps" - coming up with unnecessary words to sound "cool" when you don't need them, like calling what's essentially a rabbit a smeerp because Fantasy. If they're essentially men and women and boys and girls, "translation convention" will cover the words.

Now, if there's greater significance attached to sex and gender - say, if there's a morphic or cultural difference between breeding and nonbreeding adults - then you might want to come up with your own names to emphasize these differences.

If you do come up with your own terms for males and females, try to keep them both simple and easy to distinguish. (And be sure to draw your lines clearly, what you're renaming and what you're not renaming; it can be a slippery slope, not to mention a smeerphole of no return if you start writing your own languages and grammar and everything and forget to actually write the book itself...)

Personally I'd just go with 'men' and 'women', if your aliens are people more or less like us with a roughly equivalent gender binary, unless you're creating neologisms for every alien word that has a one-to-one equivalent in English. Even my non-humanoid aliens call each other man, woman, guy, bloke, etc etc.

Is for your 'Tree of Chaos' excerpt? I read it and they might as well be squirrels as simians, and I was okay with it. They had tails, faces, and, I suspect a bright-eyed quality, except, perhaps for the elders.
I'm with Albedo. There's no need to make up a new word for everything.

Consider it a translation thing: among themselves, they refer to each other as man, woman, the words we use for family members, and various words for degrees of friendship. The book is translating it all into the reader's language.
There is no particular need to make up a word for 'male of the species' or 'female parent's female sibling'. They are using 'man' and 'aunt', we are just not hearing the original.
You only need a word if there isn't a word, and you're going to use it a few times. If it's only going to come up once, just describe it.

Oh, and use 'hands' or 'furry hands' rather than 'paws', if their culture has developed crafts and manipulative skills. 'Paws' sounds clumsy and unskillful.

If they are playing dice, they are guys. Who else plays dice?

I might go male/female rather than men/women. Men/women does imply human a bit.

It's kind of your call. I've seen novels take different approaches to how they label nonhuman male and female characters. I suppose it depends on foreign you want them to feel and on how much you are "translating" their language into modern English. Some writers are adept at making up new words for concepts particular to an alien culture, and it adds richness to their stories. But if the terms don't quite click, it can detract from them.

How do gender identity and the perception of gender roles play out in your society? If it is similar to modern western perceptions, then it might make sense just to go with "men and women." But if they are appreciably different, or if you want to emphasize the differences between their nature and biology and ours, using different terms for people of particular genders and ages may make sense.

Also consider all the slang terms we have for male and female people of different ages, social standings, roles, relationships, and esteem. Ladies and gentlemen vs women and men vs gals and guys vs goodwives and goodmen vs wenches and (is there even a male equivalent here? The lack of gender equivalencies for some terms also says something about a culture).

This might be something where you just need to make a choice and write it the way that feels right to you while remaining open to feedback from eventual critiquing partners or beta readers.

Feel free to throw them in occasionally as a reminder it's not Earth, but avoid using too many fictional words and titles. The reader will become confused having to keep track of them all. Remember, regardless of the setting the narrator of the story is speaking to the Human reader, so keep it simple. Try using terms that are recognizable but not common. For instance, my aliens were enjoying a fermented vegetable beverage so I simply referred to it as a "ferment".