What's the advantage of Mantis Blades when you can just equip a Katana? And what's the advantage of the Monowire, which seems to do less damage than just equipping a melee weapon?

Monowire lets you kill instantly from stealth, jack in to hack from range and also has a longer range than a melee weapon (it can hit multiple opponents to boot). Base damage is low, but it builds charge the longer you have it equipped without using it. Since damage is based on Cool rather than Body or Reflexes it's basically ideal for a high crit stealth build.

Mantis blades are quicker to attack with than just about every other melee weapon, gain +3 damage per point you have in Reflexes and benefit from the blade perks.

The legendary versions of both also have three mod slots to play with.

How can I hack from range with the monowire? What button do I have to press?

He's a little off on the monowire with the hack from range. Everyone can hack from range, it's not the monowire that allows it.

But to answer you're basic question, you need a pretty decent board to allow you to do all the hacks, and alot of the hacks are gated behind perks in the Int tree. Realistically if you're a netrunner you don't need the monowire. The monowire is just a cool extra.

I remember in the initial gameplay footage, they used the monowire to hack from afar and you could only use quickhack when you had jacked into an enemy from the same group up close from stealth (kind of what now is Breach, but that couldn't be used from range either). Seems like they changed that a lot, which removed the main use of the Monowire.

Actually the damage is based off of cool and body and it benefits from the blunt weapon perks.

The biggest advantage for mantis blades is that they don't take one of your three weapon slots.
So little slots is very annoying. I'm playing on PC and I have a lot of buttons.

Well, you can always change your weapon slots during combat, so that's only a nuissance. The only things you can't do during combat is changing armour and consuming food.

AFAICT all the arm mods are just pretty replacements for other weapons, with maybe a slight extra effect (mantis leap, monowire multiple targets, launcher infinite but slow/inaccurate ammo) that don't take up a quickslot....

on a whole only the launcher arms seem like a really good deal, since there's a mod for them that is ridiculously OP and I haven't seen any equivalent elsewhere (Tranq ammo if you're wondering, one shots psychos)

One of the main advantages is that you can't be disarmed and you get to keep them in areas where you need to hand over your weapons, such as Clouds.