This character is a Private Use and has no script assigned.
The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it is written from left to right. When changing direction it is not mirrored. U+F022 does not participate in line break calculations.
The Wikipedia has the following information about this codepoint:
In Unicode, a Private Use Area (PUA) is a range of code points that, by definition, will not be assigned characters by the Unicode Consortium. Three private use areas are defined: one in the Basic Multilingual Plane (U+E000–U+F8FF), and one each in, and nearly covering, planes 15 and 16 (U+F0000–U+FFFFD, U+100000–U+10FFFD). The code points in these areas cannot be considered as standardized characters in Unicode itself. They are intentionally left undefined so that third parties may define their own characters without conflicting with Unicode Consortium assignments. Under the Unicode Stability Policy, the Private Use Areas will remain allocated for that purpose in all future Unicode versions.
Assignments to Private Use Area characters need not be private in the sense of strictly internal to an organisation; a number of assignment schemes have been published by several organisations. Such publication may include a font that supports the definition (showing the glyphs), and software making use of the private-use characters (e.g. a graphics character for a "print document" function). By definition, multiple private parties may assign different characters to the same code point, with the consequence that a user may see one private character from an installed font where a different one was intended.