"Painstaking" means done with great care and patience, meticulous and careful. To provide further help, "hapless" means hopeless, unfortunate, unlucky. 

A "hazard" is a danger, so something that is "hazardous" is dangerous. To provide further help, "unnerving" means troubling, worrying; "urging" means begging, pleading.

For the word particular, do not be confused by the "part" portion of the word. The word "particular" is not primarily concerned with being a part (in contrast to being a whole). Instead, something is particular when it is specific. For example, whenever you say, "I have a particular color in mind," this means that you actually have a specific color picked out. You are not undecided. Thus, the best option given here is "distinct."  Something that is particular is also distinct. The word can also be used to describe someone who is very picky.  A person who is "very particular" is very picky—he or she wants something very distinct. 

Whenever something is "hilarious," that thing is very funny. For this question, the best option will stress the very. That is, the best option will be one that expresses the idea that a hilarious thing is not merely "amusing" or "funny." It is, instead, "hysterical"—very amusing.

Whenever something is "enticing," it draws your attention and makes you desire it. Sometimes, we talk about one person enticing another person to do something or go somewhere. Whenever someone or something entices you, it "invites" you to come closer to it. Put another way, we can say that it "attracts" you. Hence, "attractive" is a good synonym for "enticing."

Whenever something happens "occasionally," it does not happen on a regular schedule. It is an irregular occurrence. Hence, you could say, "Rupert's occasional remarks about politics annoyed his family, but they were thankful that he didn't talk about the topic much." To be "occasional" is to happen "only on occasion." (Related words help us to memorize, of course!) Thus, the only option that expresses this idea of being irregular is "random."

Whenever something is expansive, it covers a large region—either physically or metaphorically. Thus, "expansive" knowledge of a topic is a very broad knowledge, covering many aspects of the topic. An "expansive" plot of land is a very large territory. Thus, the best option among those provided here is "extensive."

When something is "foreign," it is distant, removed, and likely unknown. A foreign country is a country that is not your own country. Sometimes, you can use the word to describe more conceptual things. For instance, if someone does not know anything about a topic, we sometimes say, "That was a foreign notion to him or her." The only option that expresses this kind of foreignness is the word "exotic."

Something that is "reclusive" is something that is isolated away from other things. When a person is described as being "reclusive," that person lives in a solitary manner, away from other people. "Seclusion" is the state of being isolated in this manner. Hence, it is an acceptable synonym.  A good example of "reclusive" in a sentence would be, "The old man decided that he wanted to live his last days in a reclusive manner, staying in his house and reading the books that he loved, undisturbed by other people."

The word "omnipotent" comes from the combination of the prefix "omni-", meaning all or totally, and the base "-potent," meaning powerful. Whenever someone is described as being "all-powerful," that person is not merely capable or able to do things. He or she is utterly unstoppable. Therefore, the best option provided here is "unconquerable."