Either +1 (strongest possible positive correlation between the variables) or -1 (strongest possible negativecorrelation between the variables).
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A correlation coefficient of 1 or -1 would be the highest possible statistical relationship. However, the calculation of correlation coefficients between non independent values or small sets of data may show high coefficients when no relationship exists.
1 would be the strongest possible. 0.353 seems to be on the weak side. Above 0.4 or 0.45 may be strong enough.
positive correlation-negative correlation and no correlation
The correlation can be anything between +1 (strong positive correlation), passing through zero (no correlation), to -1 (strong negative correlation).
No, The correlation can not be over 1. An example of a strong correlation would be .99