Learn Swedish: Hon sa att hon ville dölja sanningen. - She said that she wanted to hide the truth.

This is a rule called backshifting, which happens in indirect speech. Because the main reporting verb is in the past tense (sa), the verb in the "that" clause (att hon ville...) must also shift one step back into the past. Even if her desire to hide the truth is still true right now, Swedish (like English) changes "wants" to "wanted" to match the tense of "said".

I usually learn that the past tense of säga (to say) is sade. Why is it written as sa here?

Sade is the formal written past tense, but in spoken Swedish and everyday writing, it is almost always shortened to sa. You will see and hear sa constantly, and it is perfectly correct to use unless you are writing a highly formal or academic text.

The English translation says "wanted TO hide". Why isn't there an att (to) before dölja?

In Swedish, modal verbs and a few other common verbs expressing desire or intent—like vill/ville (want/wanted), kan (can), and ska (will)—are followed directly by the bare infinitive of the next verb. You never use the infinitive marker att after them, so it is simply ville dölja.

How is the word sanningen (the truth) built?