the audience was/were applauding heartily in their seats//bring sth to an end/bring an end to sth
1.
While the dancers were performing on the stage, the audience was/were applauding heartily in their seats.
-Between the be-verb of was and were, which is correct here? Is audience a singular or plural noun?

2.
The battle finally brought the war to an end.
The battle finally brought an end to the war.
-Are the two sentences above all correct? Is there any difference between “bring something to an end” and “bring an end to something”?

Question

the audience was/were applauding heartily in their seats//bring sth to an end/bring an end to sth
1. 
While the dancers were performing on the stage, the audience was/were applauding heartily in their seats.
-Between the be-verb of was and were, which is correct here? Is audience a singular or plural noun?

2.
The battle finally brought the war to an end. 
The battle finally brought an end to the war. 
-Are the two sentences above all correct? Is there any difference between “bring something to an end” and “bring an end to something”?

Answer

1. 
In this instance it would be better to say "While the dancers were performing on the stage, the audience applauded heartily in their seats." The first instance of were dictates that you wouldn't use applauding. Audience in this instance is plural as later on in the sentence you have the word "their".

2.

Both sentences are correct. There isn't a difference between the two. It's just another way of saying the same thing. To decide which one you would use you normally would look at the greater context of the paragraph.