It is permissible to touch the mobile phone or tape on which Quran is recorded, and it is permissible to read from it without wudu.

You can pray with nail polish unless the nail polish contains a substance that prevents water from reaching what is beneath it.

If you cannot perform wudu, you can do taymmum. But if it is too difficult to do tayammum, then it is permissible to pray without wudu and tayammum.