Have is the root verb and is used alongside the pronoun I / You / We / Ye and They and plural noun. Generally, have is a present tense word. Has is used alongside the PRONOUNS He / She / It and Who and SINGULAR NOUNS.

Three-quarters of the hostel is a singular noun because it refers to a part of one object. Three-quarters of the students is a plural noun because it refers to more than one student. 

Hence the sentence would read;
Three-quarters of the hostel has been painted and three-quarters of the students have moved in.