Can I use higher rated capacitor and larger package (for capacitors, resistors, etc?)
C4 is exposed to the externally driven EXT_5V input.  I suppose that the designer wanted to ensure that an input higher than 5V would not damage the capacitor.  Note that the regulator AMS1117 is capable of handling a 13.8V input.
C2 is only exposed to the regulated 3.3V output but it is likely picked to match C4 and reduce the number of different parts in the design.  It's perfectly OK to use a capacitor with a higher rated voltage in place of a lower voltage one.
C15 sees only the 3.3V regulated output and doesn't need to be any higher voltage than that.  Why did they pick 6.3?  Probably because they wanted some margin on the spec or perhaps just had those readily available.