What are the advantages and disadvantages to chain wax?
I suspect that it's cheaper for the manufacturer. Or if they're advertising it, it may just be a market differentiator. Regardless, leave it there rather than trying to remove it because it's right inside the chain where you need it. By all means wipe off any excess on the outside, but don't use a chain cleaner.

The different types of chain lube have been discussed at length on the web and elsewhere, and to the best of my knowlege the definitive answer is "it depends".

Broadly: oil-based (wet) lubes are more water resistant but attract gunk and turn into black sticky goo on your chain, grease-based (wet) lubes are more water and mud resistant but attract even more gunk, and wax (dry) lubes attract little gunk but wash off more easily. You also get various additives (usually teflon) to reduce friction. Then there are solvents used to remove gunk, like WD40 and kerosene. Despite sometimes being called oils, they are not useful as lubricants except in the immediate "stuck bolt" sense - they evaporate very quickly.

The consensus seems to be use wet lubes in the wet, dry lubes in the dry, and caution when discussing the subject.