Poirot seems to get along well with amiable, good-hearted (albeit slightly immature) young men– at times, he comments on Hastings' "childlike" demeanor. I think (SPOILERS) that there are other reasons why Poirot doesn't care so much for Franklin...
Yes, there are many references– albeit fleeting ones– to Miss Marple's family throughout the canon. Anne Hart expanded upon the dozens of references to compose The Life and Times of Miss Jane Marple. Her beloved uncle is mentioned in "Strange Jest." Cousin Fanny (who had a pronounced stutter) is referenced in At Bertram's Hotel. Though Hart thinks Miss Marple has only one sister, "The Thumb Mark of St. Peter" indicates that Miss Marple had at least two sisters. Another reference indicates that Miss Marple's father was probably a clergyman.
You're welcome! It's not completely clear, but I think Mrs. Inglethorpe planned to write another will, probably in favor of her stepson Lawrence, since she just quarreled with John. However, she died before she could write up a new will.
Of course, her solicitor makes it clear that he wasn't completely sure if Mrs. Inglethorpe understood the laws of inheritance...
I'm not sure who "Irene" is. Here's what happened in Styles.
Mr. Cavendish had two sons, John and Lawrence, with his wife.
The first Mrs. Cavendish died.
Mr. Cavendish married Emily.
Mr. Cavendish dies. Under the terms of the will, Emily is owner of Styles for life (Under the terms of firstborn son inheritance, John inherited Styles outright once his stepmother Emily died) and is given most of her husband's money (Some of that money becomes hers outright, but a large sum of that cash inheritance from her late husband goes directly to Lawrence when she dies.).
Over the next few years, Emily Cavendish changes her will annually. Right before her second marriage, all her cash goes to John, the reasoning being that Lawrence will get a huge sum of money from his late father's estate, and John will need a lot of money to keep up Styles. (This does not include several tiny bequests left to servants.)
Emily marries Alfred Inglethorpe. Under the law, if she doesn't have a will, Alfred will inherit all the cash Emily owns, although Styles still goes to John (though he wouldn't get any additional money to run it) and Lawrence gets the cash earmarked from his father's will.
Emily makes a secret will right before she dies after quarreling with John about his suspected relationship with a pretty farmer's wife, but does not register it with her lawyer. In it, she leaves all of her considerable money to her husband (a couple of snooping servants found the will and read it).
***MAJOR SPOILERS FOLLOW***
Emily discovers the revealing letter from Alfred to Ms. Howard. Realizing her husband may want her dead, she burns the will. Technically, this doesn't change the basic balance of inheritance, but if her husband is convicted of killing her, then the money would go to her next of kin, probably either John or both John and Lawrence, depending on the law, which I am not certain about right now.