Is it correct to think that if I say I have been ill for a week it could both mean I am still ill or I just got better? I thought that if you have recovered you should say I was ill for a week.
While those might mean the same for the laymen, from a medical point of view, there is a difference between illness and sickness. Medical sociology has long made the distinction between illness and sickness. Illness is the objective diagnosis that an external impartial observer is able to make based on the constellation of symptoms which the patient presents. Sickness is the social role that ...
In this case it depends whether you mean the common cold, which is an infectious disease, or low temperature. He is suffering from a cold and He is ill with a cold are both correct, and mean "he has contracted the disease". He is suffering from cold (without the article before cold) is also correct, but this means the air temperature (or perhaps his body temperature) is dangerously low ...
I'll is a contraction of I will. These types of "apostrophe words" are called contractions (though be aware that there are other reasons to use apostrophes besides forming contractions). The apostrophe indicates that one or more letters were removed, thereby shortening, or contracting, the word. In this example, I (wi)ll = I'll As kb90 mentions, contractions are generally considered less ...
There is a lot of overlap between the "will" future and the "going to" future. In many situations, both are possible and both are correct. In the examples you give "I'm going to be in London next week" is correct. And so is "I'll be in London next week." The difference in meaning so small that it doesn't matter. "Going to" tends to be used for future events that will occur as a result of ...