Learn French: Nous ne savions pas qu'elle était enceinte. - We didn't know that she was pregnant.

This is the rule of sequence of tenses (concordance des temps). Because the main verb savions is in the past, the reported clause must also shift back to the past. The original fact she is pregnant (elle est enceinte) shifts back, so est becomes était. In French, you must use the Imparfait here even if the pregnancy is still ongoing today.

Why is the first verb savions in the Imparfait and not the Passé Composé (avons su)?

We use the Imparfait (savions) to describe an ongoing state of mind in the past. It translates to we were unaware over an unspecified period of time. If you used the Passé Composé (nous n'avons pas su), it would imply a sudden completed event, meaning we failed to find out at a specific moment.

Does the adjective enceinte change depending on the subject?

enceinte (pregnant) is an adjective, so it must agree in number. If the subject were plural (elles), it would become enceintes. However, because of its meaning, it naturally only applies to feminine subjects, so you will never need a masculine form.

Is qu'elle just a faster way to say que elle?