What is the singular (mufrad)?

Mufrad here is the number term — one, as against the dual's two and the plural's three-plus. (Grammar reuses the same word elsewhere: a khabar can be 'mufrad' meaning not-a-sentence, and the munada can be 'mufrad' meaning not-in-idafa; keep the contexts apart.) Number-mufrad is the citation form: dictionaries list it, and the dual and plurals are manufactured from it.

مُفْرَد (mufrad) does three different jobs in this guide, and they are easy to mix up.

1. Number — one of something, against the dual and the plural. That is this page. 2. In i'rab — a single word rather than a phrase or a clause, as in a khabar mufrad. 3. In the vocative — a called noun that is not a mudāf, even if it is plural: يَا رِجَالُ.

Same word, three scales. Read it from what it is being contrasted with.

Why does mufrad seem to mean different things in different chapters?

Because it does. It marks one of something against the dual and the plural; it marks a single word against a phrase; and elsewhere it marks a word standing alone against one that is annexed to something. Always read it against whatever it is being contrasted with on that page.