Source : <http://www.huffingtonpost.com/entry/man-shares-photo-that-perfectly-shows-why-he-loves-his-hardworking-girlfriend_5697bf18e4b0ce496423637b> 

In the article ;

> 
> This is how I found her tonight. I'm so proud of this woman I could burst. 
> 
> 
> 

I am fine with this sentence except the word burst, what could it mean?

Also in the same article :

> 
> "I'm gonna take all of y'alls advice and marry the sh\*t out of her," he wrote.
> 
> 
> 

What does the phrase (the sh\*t out of her) mean? Also, how polite is it?