#CJam, 254 bytes

An example answer, not golfed.

{{['{\"_~}{{[1$'{@\"_~}"{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}_``1>W<"\"]s\~=}_~}"@]s}_~}{{[1$'{@"_~}{{[\"_~}\"2$+'{@\"_~}\"]s`\"{{['{\\\\\"\+\"]s}_~}\"+~1$~{L}@~!&}_~}"]s\~=}_~}{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}

The 3 functions are:

{{['{\"_~}{{[1$'{@\"_~}"{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}_``1>W<"\"]s\~=}_~}"@]s}_~}

{{[1$'{@"_~}{{[\"_~}\"2$+'{@\"_~}\"]s`\"{{['{\\\\\"\+\"]s}_~}\"+~1$~{L}@~!&}_~}"]s\~=}_~}

{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}

A and F take no parameters and return a string. B, G and C take a CJam block as parameter and return 1 for truthy, or 0 for falsey.

CJam, 254 bytes

An example answer, not golfed.

{{['{\"_~}{{[1$'{@\"_~}"{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}_``1>W<"\"]s\~=}_~}"@]s}_~}{{[1$'{@"_~}{{[\"_~}\"2$+'{@\"_~}\"]s`\"{{['{\\\\\"\+\"]s}_~}\"+~1$~{L}@~!&}_~}"]s\~=}_~}{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}

The 3 functions are:

{{['{\"_~}{{[1$'{@\"_~}"{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}_``1>W<"\"]s\~=}_~}"@]s}_~}

{{[1$'{@"_~}{{[\"_~}\"2$+'{@\"_~}\"]s`\"{{['{\\\\\"\+\"]s}_~}\"+~1$~{L}@~!&}_~}"]s\~=}_~}

{{["_~}"2$+'{@"_~}"]s`"{{['{\\"\+"]s}_~}"+~1$~{L}@~!&}_~}

A and F take no parameters and return a string. B, G and C take a CJam block as parameter and return 1 for truthy, or 0 for falsey.