The preferences with the Notify with selector have corresponding code inspections that notify you if this aspect of the code style in the inspected scope differs from the the preferred style. Using the selectors, you can configure severity levels of the inspections.
The preference in this section defines whether the 'public' modifier should be used explicitly.
Preferences in this section define how to handle aliases.
Prefer adding module aliases... specifies whether to use non-qualified type names and add the necessary module aliases or use fully qualified type names.
Relative file reference style in 'require' specifies whether or not to use the leading ./ characters. For example, import X = require("file1") or import X = require("./file1"). If you choose Relative to root folder, you can specify the path to the root folder on the Code Editing | TypeScript | Generated Code page of ReSharper options.
Preferences in this section define whether and when types should be specified explicitly and whether the implicit 'any' is allowed.
The preference of using implicit 'any' can also be configured in project settings. If the implicit 'any' types are not allowed in the project settings, they are always highlighted as errors independently of your code style preferences.