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Do the functions provided by this plugin capture any error messages generated by the specified function?

No.

Why would I use any of these functions instead of checking if `function_exists()` directly?

The functions provided by this plugin provide a more concise syntax for checking for function existence (using function_exists() under the hood). _sfce() will both echo and return the echoed value, which may be of use in certain circumstances. And also, since the name of the function to be safely called is passed as an argument, it can be easily and more concisely be parameterized.