Please help me correcting these sentences

Hi, I am learning new vocabulary, and I would appreciate if you could correct the following sentences for me. Thank you!

1) they passed by and completely flouted us. (They passed by and scorned us. --To be honest I have never heard the word flouted and I have spoken English all my life.  I had to look it up.)
2) the politician is trying to coax people into voting on him. 
3) he is really lax on his students.
4) Mr. Thomas exuded kindness and respect.
5) This cake is supremely good. (The cake is really/very good.  OR This cake is delicious.)
6) His overweening attitude disgusts me. / He is overweening. (again, overweening is unnatural.  His arrogant attitude disgusts me.)
7) We cannot tar everyone with the same brush just because of one person misbehavior. (Interesting.  This must be an old idiom.  I've never heard it.)
8) This city has been invaded by a heat spate these days. (heat wave instead of heat spate. )
9) He is and always been a righteous person. 
10) Everyday she dresses up like going to a party, she is really conceited. / She thinks she’s the best, she is a conceited person. (She is so conceited that everyday she dresses up like she is going to a party.)
12) The president conveyed that the war is over. (The president announced that the war is over.)

Good job!

1) flout is usually a transative verb
ex. They flouted their disregard for the law.

5) grammatically correct but sounds strange.
change to --> This cake is the best.

6) used correctly, but highly formal. Arrogrant is better for everyday use.

7) person's
I usually hear tar used with the idiom "to tar and feather".

8) spate is usually used as "spate of ____"
ex. ...by a spate of heat these days

10) like -she is- going to a party;she is really conceited
You can't use a comma by itself between 2 independent clauses.

Please help me correcting these sentences

Hi, I am learning new vocabulary, and I would appreciate if you could correct the following sentences for me. Thank you!

1) They passed by and completely flouted us.   This word is not used that frequently in the United States.  When used it generally is used to indicate that someone has disregarded some rule or law.

2) The politician is trying to coax people into voting for him.

3) He is really lax with/on his students.

4) Mr. Thomas exuded kindness and respect.   Good use of this word in the past tense.

5) This cake is supremely good.  Although there is nothing wrong with this sentence, the word supremely generally isn't used to describe such small things as a cake, but to describe something bigger, and more important such as in this sentence...James Bradley chose the most appropriate tasks, and executed them supremely well, with the indispensable aid of John Bradley.

6) His overweening attitude disgusts me. / He is overweening.  I have never heard this term used, better would be arrogant or conceited.

7) We cannot tar everyone with the same brush just because of one person's misbehavior.  Don't forget ...'s...to show possession.

8) This city has been invaded by a heat wave these days.   You would use the word spate to indicate a large increase of actions and is generally used with ....a spate of...such as.....A spate of burglaries is being fueled by drug use....a spate of burglaries....a spate of deaths.
9) He is and always has been a righteous person. 

10) Everyday she dresses up like she is going to a party, she is really conceited. / She thinks she’s the best, she is a conceited person.

12) The president conveyed that the war is over.