1) Showing manners is important because it presents a sense of character, and privilege.
2) Chivalry does seem to still exist in today's day and age, with men and women being expected to present themselves and act certain ways, especially in different specific settings.
3) -Say please -Say thank you -Say excuse me -Sit properly (no open legs)-don't put your elbows on the table-call adults M'am and Sir
4)The most important manners one can show are saying thank you, because it shows appreciation and gratefulness, and talking to elders with respect, because it shows that you know your place, and aren't greedy/are thankful for them, and their time living as compared to yours.