HEC requires name consistency throughout from NIC to final degree (of your and father's name). Ahmad and Ahmed for eg does not raise any objection. Also caste like Khan, Bhatti etc can be omitted. My brother had these issues but HEC Lahore office attested them without objection. Maybe Lahore office is lenient, I don't know.

Your case is a bit different as Hussan and Hussain are two different names. Last time I got the visa without any attested degrees (although my name is consistent throughout). Some visa clerks at embassy are lenient. I heard that female clerks reject applications more frequently so better ask other candidates in embassy to know which clerk is more lenient. Prefer male clerks if other candidates say so.

Also I do not know if visa clerks match your name on passport with that on degrees but details must match on admission letter or it could lead to rejection. Remember if they accept you are through if not then you can't do much about it.

Try to do things as early as possible. If you are late for University even if you get visa then you maybe rejected for admission. Late visa is useless in other words. So I suggest you get your docs ready particularly police certificate (it takes 1 to 2 weeks). Pay agents if you can afford. Its not the best advice but agents can expedite the process.