TASK DEFINITION: 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.
PROBLEM: 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?.

SOLUTION: '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.

PROBLEM: When it comes to cities and boats named after saints, it seems that 'Santa' is always female and 'San' is always male. e.g. Male Saints: San Diego, San Francisco, San Antonio Female Saints: Santa Barbara, Santa Maria So why isn't 'Santa Claus' a woman like all the other 'Santa's?.

SOLUTION: The city names you quote are all derived from Spanish, where 'San' (or 'Santo', as @tchrist clarifies below) is the male inflection and 'Santa' the female one. However, Santa Claus isn't derived from Spanish, but from Dutch, where it was originally rendered as Sante Klaas, and was modified to Santa when it was adopted into English (and from English, to the rest of the world). Here's Etymonline's take on it: from dialectal Dutch Sante Klaas, from Middle Dutch Sinter Niklaas 'Saint Nicholas,' English, like all other languages, borrows words from many sources, and they often carry over remnants of their original grammar or usage, even when it makes for inconsistent usage in English.

PROBLEM: These two seem very similar. What are the major differences between the two? For example, in the following sentence, Substitute the lesser punishment for the greater one. Can one use 'less' instead of 'lesser' here?.

SOLUTION:
Less refers to quantity, lesser refers to quality. Your sentence could be rephrased as 'substitute less punishment for more punishment.' Here we are saying that the amount of punishment is smaller. But if you say 'substitute the lesser punishment' you are saying the type of punishment is not as severe. Forty lashes is less punishment than 100 lashes. Being pelted with rotten tomatoes is a lesser punishment than being pelted with rocks.