generally means "imperial" as in higher alcohol and stronger flavors and larger quantities of malts to keep the alcohol flavor in check. Most are 7.5-10% alcohol so doesn't take much to get intoxicated.
Just more. Typically, enough to place it a percent or two about the style guide for the base beer. There are some brewers that do "same grain, half the water" beers. MacPelican's Wee Heavy is an example, it's 8% vs the 4.7% for the Scottish Ale.
It varies based on what the double modifies, and you have 2 good examples. A double ipa is basically an imperial IPA--bigger (higher OG, and higher ABV, and usually hoppier). A double chocolate stout usually gets some chocolatey flavor from the grain and adds some chocolate along the way as well, and it's generally not any bigger than a regular chocolate stout (just more emphasis on chocolate).