Can I create just one design which the printing company can use for
various sizes or should my designs be dimension-specific?
That would depend on what the printer wants and if your "design" is just a single logo on a box or if you're designing a full custom color box like so:
Design from vandelaydesign
Also, how do I create layout for the gift box with the top and sides?
The printer may have a template on this or spec to provide you on how to setup your document.
Can I download a template from somewhere?
Again, I would advise contacting the printer but there are some out there that provide templates and I've seen some go to other printing services and use their templates as a starting point.
The box is supposed to be glossy. Should I give the glossy effect in
Illustrator or just ask the printing company to print it on glossy,
metallic paper for the effect?
The printer may be able to provide a sample for you.
How do I create metallic effects in CMYK?
Typically its just a color that is called out as a metallic. In the rip or platemaking process you will have to make sure the metallic layer is defined.
A little self promotion on the printer topic and it may be helpful: What should you ask the printer?