Do planets have effect on velocity of Earth? There is method for finding extrasolar planets called Transit-timing variation. If I understood correctly, exoplanets accelerate or decelerate each other (according on their position), so we can observe irregularities in transit times of some exoplanet.
Now, for our solar system, can we observe similar effect here? Why time of Earth's orbit around Sun is always 365.256 days, even though other planets are always in different places? Shouldn't Earth year be always differently long?
The Milankovitch Cycles which explain the glacial and interglacial phases of the Ice Age include changes in the Earth's orbital eccentricity (which implies a change in the variation of the velocity even if the orbital period remains roughly constant), the primary contribution to which is the gravitational influence of Jupiter and Saturn.
Since our Solar System is much more widely-spaced than the typical Kepler systems, and the planets aren't in resonant orbital configurations, the variations take place over much longer timescales and have relatively small amplitudes.
Planet-planet interactions are also observed for other planets. As an example, Park et al. (2017) list various contributions to the perihelion precession of Mercury, the bulk of which is due to perturbations from the other planets (principally Venus, Jupiter, the Earth and Saturn). The famous contribution from general relativistic effects amounts to about 43″/century out of a total 575″/century.