For all practical purposes, your Application's process will never be executing as uid=0 or root, as it has irreversibly changed to an ordinary user ID before a single line of code written by you executes.
When people make "root" apps, they are not changing the application process itself back to root - that is simply not possible. Instead, what they are doing is executing a new helper process which runs as root. Underneath the java level, this is ultimately done by calling an exec() family function on a file which has the setuid bit set. This file might either be the helper program itself, or more commonly it is a "root shim" such as a hacked "su" which in turn runs the specified helper program as root. Such a helper program is almost always native code, and is probably not registered with the Android framework to be able to utilize Android-level functionality.
System Applications do not run as root either. What they have that third party apps do not is special Android-level Permissions which cause platform services that do run as root or other privileged user id's to privileged things on their behalf. A few android permissions can also confer membership in user groups which have special access - some of these are available to third party apps (Internet permission for example) and some are not.