Learn Spanish (Spain): ¿Todavía no has comprado la batidora?

Todavía no translates to "not yet" or "still haven't," expressing that an expected action hasn't happened. Ya no means "not anymore" or "no longer." If you asked ¿Ya no has comprado...?, it would confusingly sound like "Have you stopped buying...?"

Why is the present perfect (has comprado) used here rather than the simple past (compraste)?

In Spanish from Spain, the present perfect is strongly preferred for actions that have an immediate connection to the present moment, even if the timeframe isn't explicitly stated. Asking ¿No has comprado...? implies the expectation to buy it has current, ongoing relevance.

Is batidora the standard word for blender in Spain, or can I use licuadora?

In Spain, you should use batidora for a blender or hand mixer. If you ask for a licuadora in Spain, you will get a juice extractor instead, whereas in much of Latin America, a licuadora is a standard blender.

Can I put todavía at the end of the sentence, just like in English?

Yes, you could perfectly say ¿No has comprado la batidora todavía? Putting todavía no at the start of the sentence is very common and simply puts a bit more emphasis on the speaker's surprise or impatience.