Diese Reihe beantwortet viele typische Kinderfragen.

In a main clause, this is the proper way how to build up the sentence: S-P-O (subject-predicate-object). For emphasis, you could rephrase to O-P-S.

If you then insert a relative clause, this does not affect the structure of the main clause. The subordinate clause does not take any position of the main clause:

Diese Reihe, welche von Redakteuren der Süddeutschen Zeitung geschrieben wurde, beantwortet viele typische Kinderfragen.

Consequently, the same is true when the insertion is a participle phrase as in your question. Thus, your sentence (b) is correct.

If, however, you start your sentence with the participle phrase, this affects the word order as it would be affected with any kind of subordinate clause. If a subordinate clause is preceding the main clause, then it is considered as position 1 of the main clause:

Position 1 of main clause         | Position 2 | Position 3, 4 etc.
Weil ich gestern keine Zeit hatte,  bin          ich nicht vorbeigekommen.

And thus, your sentence (a) is not grammatical.

Apart: Strictly speaking, the participle clause is not a subordinate clause. It doesn't have a finite verb. But they do have the same function and, in respect to the question's topic, the same rules are applied.

Diese Reihe beantwortet viele typische Kinderfragen.

In a main clause, this is the proper way how to build up the sentence: Subject-Predicate-Object.

If you then insert a relative clause, this does not affect the structure of the main clause. The subordinate clause does not take any position of the main clause:

Diese Reihe, welche von Redakteuren der Süddeutschen Zeitung geschrieben wurde, beantwortet viele typische Kinderfragen.

Consequently, the same is true when the insertion is a participle phrase as in your question. Thus, your sentence (b) is correct.

If, however, you start your sentence with the participle phrase, this affects the word order as it would be affected with any kind of subordinate clause. If a subordinate clause is preceding the main clause, then it is considered as position 1 of the main clause:

Position 1 of main clause         | Position 2 | Position 3, 4 etc.
Weil ich gestern keine Zeit hatte,  bin          ich nicht vorbeigekommen.

And thus, your sentence (a) is not grammatical.

Apart: Strictly speaking, the participle clause is not a subordinate clause. It doesn't have a finite verb. But they do have the same function and, in respect to the question's topic, the same rules are applied.