Are there any random encounters of skirmishes or fights between stormcloaks and imperials? I havent seen any yet.. It seems like the only fights I come across ones that I start myself or if I continue on with the quest.

Yep there are quite a few Iv'e seen. Also seen a few encounters of scavengers wearing a mixture of both factions with a couple of stormcloack and imperial corpses lying about

Yes these definitely should be in the game. With all the creative random events that occur in this game I am a little surprised this isn't happening considering that there is supposed to be a civil rauaging all of Skyrim.

I guess I spoke too soon. I have never seen any of this!

Try looking in Whiterun hold. I find that's the place they're most frequent.