Mine is slightly different, but I suspect the date adjustment is the same. Pull the middle knob on the right out VERY gently. You have to stop at the first click. Then turn it to set the date.
most batteries that run of a battery are controlled by a frequency crystal or electronic setting and is not adjustable
however take it to a watchmaker or jeweller as it may be adjustable using their instruments
Anon, looks like there is a defect in that model of watch, return for refund and purchase a different model.
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Jennifer, have the battery changed at a jewelers, they do not charge much as long it is not a high class place. If the battery does not fix it, then it would have to be some kind of electrical fault in watch.