You don't forfeit any earned interest in a 30 day period by not transacting in that time, do you?
So when does each 30 day period roll-over? How can you know where you are in the cycle?

Just the compounding portion.
It's a monthly compound rather than daily, I'd guess.

Peakd shows anticipated payouts in the wallet and does the countdown for you.

I followed up until you wrote "debt ratio"

(from hivetasks.com in the market info tab)

Debt ratio is the difference between currently outstanding hive, and hive that could be created by converting hbd, shown as virtual supply.

If enough hbd exists to exceed 10% of the market cap of hive were it to be converted back to hive, then hbd's stop being given as rewards and hive is given, instead.
This is on a sliding scale that begins with 1% given as hive and ends with 100% given in hive.

This is called the haircut rule, and posts on it can be found by searching that term.

We only need to worry about it when the price of hive falls off a cliff.
Were that to happen the chain has precoded responses that most folks will learn about then.

As long as the price comes back, the ship rights itself.

It was a dark couple years while we were waiting for the righting to occur the last time the price fell of a cliff.

On the bright side, you get more hive per htu when the price is low.

Can you explain what linear rewards means, (like I'm five), contrasting it to whatever the rewards were before the change?

Linear rewards means that each vote you make pays the same rewards based on your hp.

Non-linear rewards attempt to make a game of curation by increasing earlier voters' curation returns at the expense of later voters.

This serves to bring popular content to trending by rewarding the dog pile with moar.
Except that dog piling doesn't always occur on 'good' content, mostly just popular authors benefit most from this version of curation gaming.

Linear seems to cause the least conflict, at this point.
I'd prefer to find the first day gamified, and any subsequent votes out to thirty days get linear rewards.
Payouts could be at 5, 10, and 30 days before a post goes stale.

Another potential benefit of delegating your stake is to @dustbunny

I'd prefer that dustbunny not pay a delegation dividend.
I delegate to them to help others earn curation rewards and to suck up the dust from the main source of my voters, dust voters.
They said that nobody would delegate to them if they didn't pay a dividend.

Commenting on a post with questions about Hive feels a bit like stopping a random person on the street and asking them to explain to me how the economy works.

Well, that would be true, except that we are a community that encourages friendly behavior and discourages unfriendly behaviors, for the most part.

I would guess that most anybody you could ask would be friendly, at the least.

It is hard to navigate the hive, many moving parts to the math, many different cliques to explore.

Tim has been an underappreciated asset to the chain since he got here.
He did the faq's some time back, among other needed things.