Are Khajiit allowed into the cities of Skyrim? I'm not talking about gameplay-wise.

Ironically the only one throughout the entire game that manages to make it into a walled city is a Thalmor agent (great job guards...), J'zargo is in Winterhold but that is not a walled settlement. Khajiit are ''forbidden to enter the cities'', so yes I do not think Khajiit are allowed to enter walled settlements due to their bad reputation.

Yes. It's only the Khajiit Traders that can't enter cities.

From what ive gathered as stated its only the traders that aren't allowed. I've never played a Khajiit so I don't know how guards and other NPC's react.

Yes.

Only the caravans are "forbidden." Due to their association with narcotics.[moon sugar]

It's actually more of a assumption the guards have that they'll bring moon sugar in rather than them knowing as fact.

Supposedly individuals can enter, but we haven't seen any other than the Thalmor agent Hev pointed out

As much as I hate to say it Khajiits are the only race in the game that nearly entirely fit their stereotype, which is a shame. Nearly every single Khajiit in the game is involved with the Skooma trade (caravans), a bandit or a Thalmor agent.

J'zargo is really the lone exception.