Is AKG a good choice for live vocals and studio listening?

For live vocals, the AKG P5 S gives you a dynamic vocal microphone with an on/off switch. Its best supplied new price is £44. That makes it the relevant option here if you need a vocal mic rather than listening gear.

For studio listening, the AKG K712 PRO offers an open-back reference design, with a best supplied new price of £289. Open-back headphones let sound in and out, so they are generally better suited to a quiet listening space than situations requiring isolation.

The practical verdict: these are two different tools, not evidence that everything carrying the AKG badge will suit you. Pick the right type first; then, if possible, try the microphone with your voice or check the headphones for comfort before buying.