Yes, Mount Everest erodes. Anything high up on Earth erodes and gets worn away by weather and water. But if the land under Mt. Everest is pushing up faster than erosion is wearing away Mt. Everest, then Mt. Everest will get taller instead of shorter.

Here are answers from ScienceLine Mt. Everest

This answer says Mt. Everest got taller in 5 days in 1998, and it was growing at a rate of 5 centimeters [about 2 inches] a year. But it says erosion is probably going to make Mt. Everest get shorter now.

Wikipedia is a good place to learn things: Mt Everest

It tells about the height of the rock of Mount Everest as compared with the height that includes the snow on top of the rock.

That's a great question! In general, erosion happens at all tall points on Earth -- all mountains are eventually eroded to form flat, low-lying areas. Mount Everest is no exception, and it also experiences erosion. How fast does it erode? That's a harder question. Making mountains takes millions of years, and eroding them down also takes millions of years. Because they erode so slowly, we don't have a good way of measuring it over the span of one year.

Yes! Mount Everest does erode. Wind, water, and glaciers can carry away material from the mountain.

Everest loses about 3 millimeters each year to erosion, which is about 0.1 inches. That might not seem like much, but that's tons of material over the time. Because India is pushing into the rest of Asia Mount Everest and the other mountains near it are actually getting taller by about 5 millimeters each year.

Mount Everest is eroding, although I'm not sure if it's possible to measure how much as the summit itself is eroding due to collapse rather than due to normal erosion (glaciers hollow out the sides of the mountain, and then the sides can't support the peak and it falls over). However, the earthquake faults that created Mount Everest in the first place are still pushing it up, too. It's a battle between erosion that grinds the mountain down and earthquakes that push it up! Seeing as it's still the highest mountain on Earth, I think we can say that so far the faults have been winning.