What is the top of a mountain called?

The summit, and mountaineers distinguish it carefully from a peak or a subpeak - a summit has to have enough prominence, meaning enough drop on all sides before rising again, to count as its own mountain rather than a bump on the shoulder of a bigger one. That threshold is a matter of convention and is argued about, which is why lists of the mountains in a range never quite agree.

Height is measured from sea level, which is itself a convention rather than a thing - the sea is not level, being pulled into hills and valleys by variations in gravity, so surveyors use a modelled surface called the geoid and different countries have historically used different ones. This is not academic: Everest's official height has been revised several times, and the 2020 joint Chinese and Nepali survey settled on 8,848.86 metres.

The last few hundred metres of a high summit are what climbers call the death zone, above about 8,000 metres, where the oxygen is insufficient to sustain human life and the body deteriorates whatever it does - digestion effectively stops, judgement degrades, and no amount of acclimatisation helps. Most deaths on Everest happen on the way down, after the summit, which is a fact worth sitting with.