Let us see choice by choice - Only 2 choices are meet expectations here and need analysis. Choice, a and b. The rest are wrong, we do not have to go in detail.
She can sing better than me but she isnâ€™t as pretty as I
(A) She can sing better than me but she isnâ€™t as pretty as I.
If it were separate sentence, then YES, She can sing better than I (do) - is correct. The insertion of BUT, joins the sentences. If there had been a choice, She sings better than I do, but she is not as pretty as I am. - Bingo, we all wud have closed our eyes and picked this one.
the absense of DO in the original sentence, made me choose A. I could have not have assumed "DO" next to "Better than I" because it is followed by "but". Whereas in standard in english, I (am/do/can) is understood, if it was the last word, to justify a verb in a sentence. (He is taller than I (am)).
Just a tip - - - I give an example in here to show that usage of "me" is allowed.
him more than me - Correct form. -----
She loves him more than I ------- Correct form as well.
But in the second sentence, the whole meaning changes. The first says, She loves the person more than she loves me. And second one says, she loves the person, more than I love him. Though I cannot relate the above example directly to the original sentence, this example is to show that "ME" can exist in a sentence.
I shall try to find a better explaination, and let you know soon. But, I hope this one helped.
Giving another SHOT