In “Ah, Are You Digging on My Grave?” The person who is digging in the grave is her dog
The most effective way to combine sentences (1) and (2) is definitely :William Shakespeare was born in 1564 in Stratford-upon-Avon, a town in England. This is the only sentence which both represents correct grammar and semantic structures. This sentence contains a complection of a direct object of the sentence as they bring one sense and can substitude each other. The structure of this sentence clearly shows that Stratford-upon-Avon is a a town in England that is totally correct. The second option lacks a comma, the next one contains improper use of participle phrase and the last one contains extra conjuction.
No they aren't proper to use in writing class they are considered slang. It would show your teacher that your not interested in sounding educated and proper.
Hope this helps!