Has the length of Earth's year changed appreciably over its history?

Over most of solar system history, probably not. The length of the year (as measured in seconds) depends on the semi-major axis of the Earth's orbit and on the mass of the Sun (and to a lesser extent, the mass of the Earth). The mass of the Sun has been practically constant post the initial formation of the Sun and solar system.

Recently (in the astronomical sense), Earth's semi-major axis is changed slightly by perturbations from the other planets. By 'slightly' I mean by a few times 10^-5 AU (Laskar et al 2004). It is possible the Earth's semi-major axis changed appreciably during late-stage planet migration. Cratering data suggests that the terrestrial planets got heavily impacted in a short timeframe about 3.9 billion years ago, termed the Late Heavy Bombardment. This bombardment was probably due to planet migration. As the giant planets moved their influence destabilized a significant number of asteroids, some fraction of which hit the terrestrial planets. Jupiter probably moved inwards by about 0.2 AU, Neptune probably moved outwards by about 10 AU. It is unclear how much the terrestrial planet semi-major axes changed (indeed, sometimes proposed scenarios for the migration have trouble avoiding destabilizing the terrestrial planets). Figuring out exactly what happened is a very active area of research.

Yes it has. u/jccwrt has an observation of the year changing, as to why is due to the Earth-Moon interaction and tides.

First two sentences:

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon), and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation.

Yes. Coral polyps produce a new layer of calcium carbonate every day, and the amount they produce is related to seasonal temperature and sunlight cycles. Study of fossil corals suggests that in the Silurian period (445-416 million years ago) the year had about 400 days in it. Since the Earth's orbit probably hasn't changed appreciably, that would mean each day was about 22 hours long.