Gallante - AR, SG, PC
Minmatar - MD, SMG, HMG,
Caldari -SNIPER, SL, FG,
Amarr - SR, LR, SP

Have I missed any?

Our flag hangs in the Warbarge...duhhhhhhh

For the State!!!!

FLaylock? thanks though:)

My bad, flaylocks are minmatar.

Basically,
Gallante are short range plasma tech, they rely on being abld to rock up and tank a significant amount of damage
Minmatar are short range, they use projectile tech like we have in RL, they reky on speed and reps for hit and run
Caldari are ultra long range railgun tech, their sheilds allow rapid repping for between fights
Amarr are long range laser tech, they dual tank for increased power to allow for maximum time in combat

Tho the lore about these things is all out there and there is a lot of it. Many sources and pages, you access most of this from Community Site http://community.eveonline.com/. Evelopedia would be one of them, then there are chronicles and stories. And within the EVE itself of course.
The Flaylock, Remote Explosives, Locus Grenades and things like Repair tools are Minmatar as well.
Then the Flux grenades is Gallente, AV grenades are Caldari.

Edit: Also most of the times, depends how the things are manufactured, you can tell which race it is by the looks and materials used.

Oh aye, I forgkt about grenades, i suppose repair tool is mini
drop uplink in amarr
nanohive is gallante
and caldari dont have eq yet, but I heardmit was the webifier!!

Nono dude, I think you are a bit mistaken here, the nanohives are not gallente, that would be caldari technology. And the repair tools are indeed a Minmatar. I know, because I am into the lore of eve for quite a long time .

They are they look more gallante in design? I suppose it makes sense wjth how caldari fight.

Aye, tho I understand why you meant it fits the gallente too, cause these two technologies have some similarities, plus you see a Gallente in game often using caldari railguns on their ships too. rails and other hybrid technologies has been shared between gallente and caldari. And caldari tend to use the missiles and rockets more. And nanohives are of hybrid tech too :D

Will the Gallente Federation having members of all races, its not too surprising to find us using whatever we can get hold of though tbh

Yea exactly. You can imagine, that every race is not tied to just 1 particular technology and that they use different things and combine them, it also depends where it has been manufactured and stuff. It can be really diverse as it would be in "real life" eve universe.