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The truth is acrylic dry faster than any other medium. Unless you are on some sort of a deadline I would recommend staying put, or using a low force hair dryer or just a simple fan. When drawing a complex drawing usually acrylics allow you to make changes, like when I was trying to create a rather difficult Rajasthani painting it helped me make many changes as I was in unfamiliar territory.

If you have applied a very thick layer of acrylic paint in your painting, You can also keep the art next to a fan, or in a dry and warm room. These methods would be less risky than putting the painting in the sun.

You can. They paint won't crack or be damaged in any way. But acrylics dry fast anyways. Unless you have a specific reason for drying the painting in the sun, I would recommend that you not do that.