You have two different question here. The first is the difference in years between earth and mercury. The answer there is that a 'year' on Mercury, defined as the time it takes to make one revolution of the sun is almost exactly 88 earth days.
Your other question is in relation to what is known as 'time dilation'. This is a part of Albert Einstein's theories of Relativity, and it basically states that the faster you go, the slower time becomes for you. However, this begins to become noticeable only at VERY high speeds, as you approach the speed of light, where time slows to a stop. It's only in the last few percentiles (say 95% or more of light speed) that an effect would be really noticeable
Scientists have confirmed the basis of time dilation by placing very accurate atomic clocks in planes traveling in opposite directions around the earth, and comparing them when they returned. The differences were in nano-seconds, but they did conform to the theory.
In the real world, even in space travel, the differences are not noticeable because the speeds are just too slow.
