Conjunctions – Usage of ‘Due To’ and ‘Because’ – Are They Interchangeable?

As is used to mean because, but it is also used when two events happen at the same time.

In "I must stop now as I have to go out." it means because, but in "She watched him as the train passed close to his house." it doesn't mean because.

As for the sentences you used as examples, both are correct.

"Due to the fact that" is an idiomatic expression often used to say "because", it does not refer to a specific fact.

First, let’s disparage all the wordy ways to express the meaning “because.” There are quite a few: “due to the fact that,” “owing to the fact that,” “on account of,” and “on the grounds that,” for example. If you use “because” instead of those beasts, you can save up to four words.

"Due to that that" is not used and would probably not be understood.