Question

Choose yes or no to tell whether each of the following describes a convenience sampling method​

Answer 1

1. No, this is systematic sampling. Systematic sampling is where you use a specifically well defined rule to generate your sample. In this case, that rule is "pick every 4th customer". In other words, if the customer number is a multiple of 4, then they are selected.
2. No, this is simple random sampling (SRS). Each school is assigned a number, and those numbers are fed into a computer to generate a list of schools to form the sample. A random number table can also be used. When comparing to systematic sampling, SRS in my opinion is the stronger sampling method in that we get a better representative sample. Consider a case where on some unlucky circumstance that every 4th customer happens to be male (refer to problem 1). That would mean males are over-represented while females are completely under-represented. This example, while a bit extreme, shows a flaw in systematic sampling. So in short, it's best to use SRS if you could only pick one.  
3. Yes, this is convenience sampling. As the name strongly implies, convenience sampling is the easiest or most convenient way to select a sample. Sheila simply looked to her left and right to get the sample points she needed. While it's tempting to use this method due to its ease, it's probably very clear that this method can be heavily biased. She should employ SRS to get a better representative sample.
4. Yes, this is convenience sampling. For the quality control manager, the easiest most convenient ladders he found were the first five closest to him. Those five ladders may or may not be representative of the population. The population being the set of all ladders in the shop. If those ladders don't break, then the manager may get the wrong conclusion that all if not most of the ladders won't break. However, his sample is not representative and there may be bad faulty ladders in the shop somewhere. He should do a SRS to address this problem. Perhaps even a cluster sample where he breaks the shop's floor area into various chunks and does random sampling based on that. A cluster sample is useful because some areas of the shop may be better or worse off compared to others. Eg: if there's a leak in the roof in one spot, or if there's more moisture, then that cluster is different from the rest that don't have such issues.

In short, we have these answers in this exact order: No, No, Yes, Yes.