Is that correct or do other circumstances need to be taken into account such as presence of cloud etc?
Can icing conditions occur below 100% relative humidity?
Do icing conditions always occur when temperature is below zero?
In-cloud icing is the most common location for icing conditions, save for the situation NorthSouth described. That can be solved by "cold soaking" the airplane - opening the hangar door and letting it "soak" in the colder air before pulling it out into any precipitation. This may still result in ice, but it is likely to be rime or mixed icing, or frost which is easy to get rid of. By not cold soaking the airframe, you're likely to get clear ice which takes a lot more glycol to get rid of. This all assumes active precipitation.
The other common area for in-flight icing that many pilots often forget is when flying in the clear, cold air below a front or TROWL. In this case the warm(er) precipitation cools as it falls, and can form ice when it hits the airframe. This can be aggravated if you're flying "the wrong way" and you're approaching the front from the warm side. This presents an interesting situation where the pilot thinks they are simply flying through the rain with a cloud base possibly thousands of feet higher, yet they're accumulating a serious amount of ice (think Freezing Rain, Freezing Drizzle, snow, hail, ice pellets, snow pellets, etc.).
Although this can happen behind a cold front, a warm front warrants a little more respect (in this specific, narrow regard) due to the slope of the front and the larger geographical area affected ahead of the front. Cold fronts do tend to have heavier precipitation, but it tends to be isolated to a few km. A warm front, on the other hand, can affect an area of 600 km or greater.
So.
1) Do other circumstances need to be considered? Yes. More than can be covered in a post. I would suggest a book titled "The Air Command Weather Manual," a review of Transport Canada's "When In Doubt" (
When In Doubt), or a viewing of any (or all) of these videos and products:
NASA Icing
2) Can icing conditions occur in less than 100% humidity? Yes.
3) Do icing conditions always occur when temperatures are below 0C? Yes and No. It is unlikely for airframe icing to occur above 0C outside of freezing precipitation. However, one must be vigilant in temperatures below 10C as local areas around the airframe and in the engine may cool to permit icing (think, carburettor icing).