First of all, thank you for making it free!

I'm completely new to ear training. Could you give some advice on what a newbie should think while doing this? For example, should I try to sing the thing in solfeges in my head, or it's considered bad practice? And if I do, should I sing the first note as Do?

So the only problem is that until you've internalized the intervals a bit better, you might get frustrated trying to sing out solfege since you might say "re" when the note was "mi" in the context of the key signature and that might reinforce a bad intervalic relationship. However you could still hum/whistle the pitches as an assistive tool.

If you’d like to make things a bit easier, you can go into the options and restrict the key signature. That way you can keep it simple and just practice in a more common keys like one major scale like C major and its relative minor, A minor.

Where I really recommend "singing" out each note is when I'm teaching my students to improvise on the piano since it creates a sort of intentionality about what you’re about to hear and sing.

For example, if they had a chord progression or melodic idea in mind but accidentally played a wrong note, they’ll notice right away because what they’re singing won’t match what they’re playing.

Whereas if you don’t sing or whistle the notes as you play your instrument, you might not notice that you’re drifting off from what you actually intended to play because within the confines of the key signature it might still sound melodically acceptable (if that makes sense).