Does time move faster depending on the size of the viewer? Does time go by faster for ant, as opposed to an elephant? Do we seem to move slower to an ant? And if that is so...would time on Earth be relatively fast as opposed to time in the Universe? 
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*I believe you are asking two questions:


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*Do different types of animals/humans see time flow at a different speed?

*Does time tick at a different speed at different places in the universe?
The answer to #1 is we would not be able to say. Because animals would not be able to say, but all humans see here on Earth time flow at the same rate approx. Though, there are drugs (mostly in sci-fi), that make humans see time flow slower. See Dredd (2012) Slo-mo drug. It would be possible, to make a drug that makes our brains act faster, and thus compared to us, time and everything else would seem to flow slower.
The answer to #2 is that according to GR, gravitational fields caused by masses do slow time down when viewed from another place with lower gravitational fields. If you try to measure the speed of light from Earth when it passes next to the Sun,  you will see it travels with a speed slower then c. This is called the Shapiro effect, and it is partly caused by the fact, that clocks next to the Sun tick slower compared to clocks on Earth, when viewed from Earth. The clock next to the sun is in a stronger gravitational field (then the Earth's field) so that field slows the clock there down compared to the clock on Earth. So what you see from Earth is that your clock on Earth ticks faster.
So the answer to your question is that clocks tick differently at different parts of the Universe, depending on the gravitational field that they are in. But only when viewed from another gravitational field.
When you look at your clock wherever you are, your clock will seem to tick normally for you. You have to compare it to another clock somewhere in the Universe to see the difference.
