How to memorize all those endings? Do the Russians really always think which case to apply?

No, of course, the Russians don’t think about cases when talking. It’s embedded in their heads – it’s just their way of thinking. The English don’t think which tense to apply – they will never mix the verbs in the phrases: ‘I’ve read it already’ and ‘I read it yesterday’, which is, by the way, Russians will use the same verb in both phases:

I’ve read it already = Я уже это читал.

I read it yesterday’ = Я читал это вчера.

Repetition is the key here. Listen to the audio regularly and try to repeat after the native speaker. Listening improves your comprehension, but repeating actually makes you think more.

Sometimes you have feeling that you understand everything, but when you try to repeat, you are confused and don’t know all the words and all the endings. So work with audio 30 min every day and eventually you will get it.