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Yes it would, but measureably diminished. Our reproducative systems usually allow for enough natural variation and genetic scrambling to promote quite a bit of change in population gene frequencies over generations. So even without classic gene mutations, genetic variation will still be produced and differentially selected. See Hardy Weinberg for more.
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Not entirely at first. If it stopped today then there is still a lot of room for evolution due to selective mating and that still causes evolution. For example, if a bug with a long horn (kind of weird) mates with a bug with no horn and the offspring are born with horns, they have the higher chances to survive due to more defenses. Wait, what am I talking about. I think I'm right. Well, I hope that helps but I do know that eventually, there would be no more evolution...nevermind. I think I'm all wrong. :(
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For a while. Evolution would work with the variation that already existed, but it would quickly disappear as we became more homogeneous and eventually stop because there is no variation left to work with and no new variation being introduced into the system.
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I'm not a geneologist but I don't think evolution would occur if mutations just up and stopped. Unless they were man made mutations. But if ALL mutations just stopped, then probably not. That being said, mutations just stopping is impossible.
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For a short time, as favorable traits that had already been developed began to spread. But long-term, evolution would cease.