Learn English – Word for groups of periods of time

I would just use "per decade" and "per century", but the words you're looking for are decennially (as in "the census is done decennially") and centennially (and millennially). See Wikipedia: Anniversary for more words.

Per Google, bifortnightly and bi-fortnightly together have been used about 5000 times on the web, frequently as objects of ridicule rather than as serious terms for "four-week-ly", occasionally as examples of misunderstanding of whether bi is a multiplier or a divider.

Although the lunar cycle is often thought of as 28 days, lunarly doesn't actually work to indicate 28 days, because the moon's sidereal period is only 27.3 days.

Regarding quadweekly and quadriweekly, I like quatriweekly or quatri-weekly better. Quadroon and quadrant, for example, use quadr- as one-fourth, while quatrain uses quatr- as four; but the roots of all of them are closely related to words meaning four.