Random sampling is important because it is much more practical to test a small group of results than a bigger whole. Say, for instance, a company wants to test the average voltage of a battery they manufacture. It would be much more practical to test 1000 randomly chosen batteries than to test 100000.
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You are correct; convenience sampling is not random sampling.
Simple Random Sample Stratified Random Sampling Cluster Sampling Systematic Sampling Convenience Sampling
That's a random question
Circular systematic sampling is a random sampling method. An example is random sampling of households. Assume that a random number generator provides the number 49 as a starting point. Starting with the household that is 49 on the target list, every nth household on the list would be sampled until the desired sample size is reached
stratified random sampling is a sample(strata) that a same and hemogenieous in group and that a different and heterogenious in group