There should have been other races added to The Stormcloaks or Imperials,Why do I see all these Dark elf farmers claiming they want to join the Legion yet there is only ONE Dark elf Legate in a random camp.

I have seen lots of different races in Legion units, as for the Stormcloaks well there I refer you back to the many other threads which cover racism in the Stormcloak/Nord ranks

The Stormcloaks aren't more racist than Nords in general, but it is mainly a Nord cause. However, one of the random NPCs who are on his way to Windhelm to join them is Imperial, and in one quest an NPC with a Breton-sounding name is believed to have joined them (I don't know her actual race, though, she might be Nord despite her name). IMO, it would have been more reasonable if the SC consisted mostly of Nords, with a few members of other races, but not many.

I think I've only seen Nords and Imperials among the nameless legionnaires, possibly some Redguards, but never any elves or beast races. There are no women in the Legion, either, except for Rikke and the captain who sends you to your death in Helgen.

Apparently there were female legionnaires in the cut content (verification?) - maybe the same is true for other races in both armies as well?

There were some Legionettes in Helgen besides the captain, one was standing near the tower that the Stormcloaks first ran to, and others were battlemages fighting the dragon. But later in the game, none are to be seen.
On soldiers of other races, there is Legate Fasendil in the Rift, who is an Altmer.

There is also an Altmer Legate in the Rift.

You beat me to it. Also many Orcs join the legion for adventure and travel. Although i cant think of any in Skyrim right now, if there even are any..

Yeah, I know about Fasendil, but among the nameless soldiers there's little or non racial diversities.

I tried to use console commands to change the random soldiers' races once... it didn't go well. I ended up with floating body parts, discoloration, and more horrors.

For science!

I once found a hostile Khajiit in Imperial Armor, I don't know if he stole it or not but there was no body nearby and his health said ''Khajiit''.