They are all OK. Although I would add some commas but that is my preference.
In items 2 & 3 we are using Due to mean because of.So lets do a substitution to see if the sentence is still OK.
It was due to his illness, (that) he could not come to school
It was because of his illness, (that) he could not come to school
Due to his illness, he could not come to school
Because of his illness, he could not come to school
Note; The use of That as a conjunction is optional although to me it sounds more comfortable to use that in the second example
that Link E.E.D.
conjunction: used to introduce a clause that reports something or gives further information, although it can often be left out: