Asking help on phrases

Hi folks,
I'm a English learner and could help me with the meanings of the following phrases?
1.the Next Big Thing

2.to have a non-uniform day

3.Better start building an ark.

4.Brush off one's coat.

5.There are a lot of family reunions and festivities here in Uzbekistan, and I always have to serve a dish that I've made myself, which means I have to stay up late to prepare my lectures, a uzbek teacher said.
(serve a dish?)

6.When you say somebody is ill, you say one "go down with" some illness or "come down with" some illness?

I would appreciate it enormously if you would help me!
Thanks in advance!
Sphinx

My opinions:

1.the Next Big Thing -- The next fad, craze or popular item/activity that interests the public. Today's big thing in the U.S. is "reality television."

2.to have a non-uniform day -- I don't know what this means. Have a day where workers can wear their regular "street clothes" rather than a uniform??

3.Better start building an ark. -- It is raining hard. It refers to Noah in the Bible. He built an ark because God told him He was going to destroy the world with water.

4.Brush off one's coat. -- I don't know any meaning beyond the literal. I have heard an expression about recovering from a problem or mishap -- "Dust yourself off and start over."

5.There are a lot of family reunions and festivities here in Uzbekistan, and I always have to serve a dish that I've made myself, which means I have to stay up late to prepare my lectures, a uzbek teacher said.
(serve a dish?) -- Dish (in this case) means a food item that requires preparation. You bring a dish with food in it -- a casserole (a dish that food can be baked and served in). An event (U.S.) where people bring food items is also called a "covered-dish dinner" or a "potluck."

6.When you say somebody is ill, you say one "go down with" some illness or "come down with" some illness? I'm coming down with a cold.

Hello! "Non-uniform day" may also be day out of the ordinary, with unusual occurrences.
----"Building an ark" could also mean "things are getting tough, trouble is coming, better be prepared".
----"Brush off one's coat" as in "Getting dressed up to go out somewhere special", perhaps?
----"Come down with" is most common, with "went down with" as an alternative ("Harry went down with a fever last night").