The bows wont work, because we already have plasma canon.
The rest will become insanely OP when a well coordinated team uses it.

The problem with a lot of these is that EVE and Dust are actually fairly hard-science universes... there's not a whole lot that I'm aware of that outright violates laws of physics... and because of that.

Flamethrowers - Dropsuits are extremely durable and designed to be fairly resistant to conventional arms fire (The extremely super-enhanced clone that 'you' are has 10 hp, militia dropsuits average more than 300 hp 30x what you have)... so you have the Gallente who use *superheated plasma fired out of focused apertures* to do 'thermal' damage, or the amarr who use a high frequency laser that does a bit of damage on its own and then ignites the very air to plasma that travels in the same channel the initial laser burst made.

Bows of any variety - No, just no. I don't care what future materials you have there comes a point when the amount potential energy stored by drawing a bow string back fails to be meaningfully converted into kinetic energy upon releasing the string, it is instead 'wasted' by doing things like producing heat or noise. The other downside to bows is that they have very low rates of fire. Now if we want to compare this to say a railgun which takes a fairly heavy solid slug and uses electricity to generate a circuit that wants to expand as big as possible and thus causes said slug to accelerate to 7000m/s in a fraction of a second you've already got a weapon far, far more damaging than a bow and it fires several hundred rounds per minute!

Lightsabers - Do you want to get sued by Lucas arts / Disney?
Mind Control - Outright isn't possible within the new eden universe, the only person ever thought to be capable of any 'psychic' ability was actually just exploiting backdoors in implants she had put in people. If you're talking about telekinesis like you described, once again not possible as eve is a *very* hard science universe 'magic' or 'supernatural abilities' do not exist.
Disc Guns - If you're envisioning a room filled with bouncing flechettes, you're severely underestimating dropsuit armor.

Remote turrets are possible, but drones are better and they are very very gallente tech.

what about a gun that shoots acid?

Turrets the only thing that looks interesting. A crossbow? This is the future where we have 17km long ships and have weapons that shoot lasers seems a bit stupid.

I keep saying that we need a dildo cannon but it keeps getting shot down.

Seriously.... you KNOW there is interest in a new BIG melee weapon. A plasma sword, a phased warhammer, power fists I dont know what but something melee!

Uhm mind control doesnt really work in new eden..

uhm we still dont have that.