Does an experiment always have to have a control group

No. Imagine you experimenting to see which brand of 3 tires had a longer-lasting tread. Your experiment would be to run all three brands and see which wore out last- you are comparing three independent variables against each other; there is no control in this case..

Yes it does. If you didn't have a control group, there would be nothing for you to compare your results from the experimental group. For example, if you were doing an experiment about the effect of nitrates on plant growth, you would need another group of plants that were given no nitrates so that you can see the effect.

Yes. You always need something to compare.

You need a group that has no changes (the control group) and a group that has one change so you can see how that one change affects what's being experimented on. Without that control group, you won't know how that change affected the subject.

Yes it does,
The control group or the (controlled variable) is needed to compare your results with the in independent variable

Well, yes, defiantly if you want it to be a truly fair test.