A control group is a group of subjects in an experiment that does not receive any treatment or intervention under investigation. The control group is used as a baseline to compare the outcomes of the experimental group that receives the treatment or intervention.
An experimental group is a group of subjects in an experiment that receives the treatment or intervention under investigation. The experimental group is used to measure the effect of the treatment or intervention on the outcome variable(s) of interest.
The number of testing variables (independent variables) that should be included in an experiment depends on the research question and the hypothesis being tested. In general, it is better to limit the number of independent variables to one or a few in order to isolate the effect of each variable on the outcome(s) of interest. This allows for better control of extraneous variables and increases the internal validity of the study. However, there may be situations where multiple independent variables need to be tested simultaneously in order to answer the research question or hypothesis being investigated. In such cases, a factorial design may be used to test multiple independent variables.