Is there Bishul Akum when using a microwave, considering that it is not cooking as it was in the times of Chazal?
It's debated by contemporary poskim (and can come up in many dairy restaurants that use a microwave to make eggs). From what I've heard (a friend of mine spoke to the OU's Rabbi Genack, who asked RSZ"A, if I recall correctly), R' Shlomo Zalman Auerbach held it was a problem (though he does not consider the microwave to be cooking vis-a-vis shabbos). My impression is that many American poskim are lenient.
in ialcut iosef shabat he brings that microwave is safek if it considered bishul. In practive we should be stringent. in regards shabat it means that something prepared using a microwave could not be reheated in a plata because it is safek that it is already cooked. while I personally understood the halacha that we posek lehumra maybe you could assume that it is safek miderabanan lecula. but this is rather bediavad and not lechatehila.