Learn English – Using commas and pronouns correctly in “Not only because, but also” construct

The correct word should be is.

You wouldn't normally say "a book are on the table" or "a pencil are on the table". Since you did not make a list of nouns or use any plural nouns, the verb should remain singular.

The basic rule is that the matter following not only should parallel the matter following but also--the two should play the same syntactic role in the sentence.

So this is clumsy:

 This not only    allows you to maintain a uniform visual style, 
      but also    ______ ___ to introduce new developers to your codebase.

To introduce is not parallel with allows you. But you may easily clean this up by moving not only

 This allows you not only    to maintain a uniform visual style, 
                 but also    to introduce new developers to your codebase.

Your other examples are a little harder to illustrate, because a) the inversion you employ when not only launches the sentence has to go away in the but also piece, and b) the also has to move; but the principle is the same:

Not only should you        be able to speak, 
but      you should also   be able to write.

Note that you can drop the but in this case. You can see the pattern more clearly without the inversion:

You should not only   be able to speak,
           but also   be able to write.
      OR
You should be able not only   to speak,
                   but also   to write.