Learn Finnish: Mikään ei ole yhtä tylsää kuin huono ohjekirja.

Yes! The pronoun mikään is formed from the root word mikä plus the enclitic particle -kään. Over time, the 'k' dropped out in pronunciation, leaving mikään. Because it contains this specific enclitic, it is used strictly in negative contexts to mean 'anything' or 'nothing'.

The current lesson is about the strict order of verb suffixes. Where do those suffixes go in a negative sentence like ei ole?

In Finnish, the negative word ei is actually a verb that takes the personal endings (e.g., en, et, ei). The main verb ole is left in the connegative form, which is just the bare stem. If you want to add an enclitic particle to the main verb (like -kaan to mean 'after all' or 'either'), it attaches to the very end of this bare stem: ei olekaan.

Since a rulebook (ohjekirja) is a countable object, why is the adjective tylsää in the partitive case instead of the nominative (tylsä)?

The adjective's case is determined by the subject of the sentence (mikään), not the noun it is compared to (ohjekirja). Indefinite or abstract pronouns like mikään generally take a partitive predicative adjective. If the subject were a specific, countable book, the adjective would be nominative: Tämä kirja on yhtä tylsä (This book is as boring).