Is it permissible for a resident in the United States, studying there, to combine the Asr prayer with the Dhuhr prayer by advancing it, given that she cannot find a place to pray and is often forced to shorten the Asr prayer due to her commitment to the study location?

The Asr prayer should not be shortened except when traveling. Studying is not an excuse to shorten it. However, if the place of study is at a qasr distance (a distance that permits shortening prayers), then it is permissible to combine Asr with Dhuhr. The general rule is not to combine them if one is a resident. If combining becomes difficult, then there is no objection to combining it with Dhuhr, provided it does not become a continuous habit. One must be careful not to be lenient with prayers in general, and the Asr prayer in particular, as it is the middle prayer (Salat al-Wusta). Furthermore, migrating to lands of disbelief is not permissible except under specific conditions, and studying in mixed-gender institutions, especially in lands of disbelief, is not permissible except out of necessity.