Dan likes to race his car fast, and he should think about safety.

Dan likes to race his car fast, or he should think about safety.

Dan likes to race his car fast, but he should think about safety.

I offered to help her down the ladder but, she refused my offer.

I offered to help her down the ladder, but she refused my offer.

I offered, to help her down the ladder but she refused my offer.

Yes - after the word 'but'.

Yes -before the word 'but'

No -the sentence is fine as it is.

You should study for the test, is a big part of your English grade.

You should study, for the test is a big part of your English grade.

You should study for the test is a big part, of your English grade.

You are a new student, and you will have to learn our class routines.

You are a new student, so you will have to learn our class routines.

You are a new student, but you will have to learn our class routines.

Do all of your homework, and you will fall behind.

Do all of your homework, for you will fall behind.

Do all of your homework, or you will fall behind.

Yes- place a comma before the word 'and'.

Yes -place a comma after the word 'and'.

No - the sentence is fine as it is because there are not two complete sentence on both sides of the FANBOYS 'and'.