1.You are assured that the goods will arrive within two weeks of the shipping date.
*①are assured②will assure In this case, use "are assured". Will assure is a future tense, but in this case the person who wrote the sentence wants the receiver to know that he/she is certain now that the goods will arrive within two weeks of the shipping date.
2.The office is currently undergoing a renovation, so we have to share the room with another department temporarily.
①undergo *②undergoing Undergoing is used here. The -ing means that something is happening now. The sentence says "currently" so we know that the renovation is happening now.
3.John is one of the best employees in the company, and that is the reason why he can be a supervisor at such a young age.
*①is②are③was④were This sentence is in present tense. "Was" and "were" are past tense. "Are" is present tense but is used for more than one person or thing. (They are, He and she are, Tom and Joe are etc.). "Is" is in the present tense and is related to the "reason". Only one reason is presented and not two or more so "is" is used here.
4.The job fair offered opportunities for job seekers to directly interview with possible employers, which had positive influence on the future cooperation.
①offer②offers*③offered④offering This sentence is past tense so "offered" is used. You can tell that this sentence is past tense by the phrase "had positive influence". "Had" is in the past tense.
5.After all résumé have been reviewed, the manager selects 3 candidates to join the final interview.
①selecting②selected*③selects④select This sentence is in future tense so "selects" must be used. Selected is past tense and if "selecting" were used the sentence would have to use "the manager is selecting".
I hope this helps!