We congratulate you on your high ambition to seek knowledge and we encourage you to learn and support correct ‘aqeedah, the ‘aqeedah of Ahl al-Sunnah wa’l-Jamaa’ah.
We do not encourage you at all, after travelling and getting the opportunity to study in al-Azhar, which Allaah has made easy for you, to give it up for something which may or may not happen.
The wise man does not give up something except for something that is better than it. Do not give up the good thing that is in your hand for something uncertain. Yes, there are some things in al-Azhar that go against the ‘aqeedah of Ahl al-Sunnah wa’l-Jamaa’ah, but not every professor in al-Azhar is like that. There are some of Ahl al-Sunnah wa’l-Jamaa’ah among them, so strive to benefit from them and learn from them, even if that is outside of the college and organized study.
There are daa’iyahs and seekers of knowledge in Egypt who are not teachers and professors in al-Azhar, but they are known for their keenness to teach the Sunnah and follow it. Strive to keep company with them and attend their gatherings.
If you come to Saudi in the manner that you describe, you will never be able to submit your papers anywhere, let alone wait until you are accepted, because you will be sought by the security forces for going against the iqaamah system. You can correspond with the universities that you want to apply to from Egypt, without losing the opportunity that is in front of you. If you are accepted, then you can decide which is best for you at that time, by praying istikhaarah and asking Allaah for guidance, and consulting some of your brothers and professors.
We ask Allaah to bless you with beneficial knowledge and righteous deeds.
And Allaah knows best.