Generate the answer for a given question. The question requires common knowledge of English. Make sure that the answer is in detail, long, consistent with the context, and requires general knowledge of English. To be less repetitive, please vary your language for each question. Give a proper explanation to answer, and if necessary, provide the definition of various terms. And conclude your answer if it's long. If you have used other resources (e.g., Merriam Webster's.) to answer the question, include citations in your answer. You don't need to paraphrase the context of your resources, but make sure that your answer is consistent and complete.

I am just wondering about the difference between: in contrast to and in contrast with.
In fact, they could be used interchangeably, however, 'in contrast with' is more common in UK English. Moreover, When we say 'contrast with', CONTRAST is behaving as a verb. Example: 'He likes to contrast his checkered jacket with plain pants' or 'his checkered jacket contrasts with his plain pants.' But when we say 'in contrast to', it is behaving as a noun. Example: 'His checkered jacket stands in contrast to his plain pants.' (As you can see, in this sentence 'stands' is the verb). (Testluv, GMAT Instructor, Beat the GMAT forum)

Suppose I tell something to my companion and I want to make sure he understands me. I thought I may simply ask 'Do you understand me?'. But recently I heard that in such cases I should ask 'Does that make sense?' instead. Is this true? Which option is appropriate to use in business communication?.
'Do you understand me?' slightly carries the implication that it is your fault if you do not understand. 'Does it make sense?' carries the implication that it is my fault if you do not understand. So politeness suggests that the latter is better.

Consider the following sentences: The last few years has seen the building of the new church. and The last few years have seen the building of the new church. As a native speaker, both of these sentences 'sound' correct to me. Is only one of them correct, are they both correct or is each one only correct in specific circumstances. This was a question one of my students asked me, so if there is a relevant grammar rule, that would be great.
Years, being plural, takes the plural form have. But the last few years, being a single span of time, takes the singular form, has. That's why they both sound okay to you. The first option is generally preferred in formal writing.