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Accidentals (sharps, flats or naturals) only change notes until the end of the bar they are in. So, the C# above doesn't affect the C in the next bar. However, flats or sharps in key-signatures affect all notes in the music, for instance the Bb and Eb above, unless "overruled" by another accidental, for example the B natural above.
There is no Cb in the key sig. In fact, Cb rarely appears in a key sig.Since there is a bar line preceding the C, any accidentals would be cancelled.So it couldn't be a C#.There is no reason at all why it should be a Cb.(Often called B, often incorrectly...) Therefore, it is played as a simple C natural, the white one on a piano.
According to the image, it looks like you might have a recording that came with the book, so I would certainly suggest listening for how it is meant to be phrased. Technique-wise, since this is a ukulele, you'll be finger picking everything. Commonly you'll see grace notes appear on the same string, which means you would use a hammer-on or pull-off by ...
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