See the Roth IRA ordering rules for distributions in IRS Pub. 590-B. Conversions and rollovers are treated as a middle ground between contributions and earnings. They can be withdrawn immediately without regular income tax, but taxable conversions/rollovers incur a 10% early withdrawal penalty for the first 5 years. Conversions/rollovers are withdrawn in a first-in, first-out basis by year, and taxable comes before non-taxable within the same year.
Now, what this publication doesn't make clear (at least to me) is that Roth 401(k) to Roth IRA rollovers are treated differently. Your contributions to Roth 401(k) become like Roth IRA contributions. But the rest is not treated as a rollover, but rather as earnings. See CFR § 1.408A-10. When you do this rollover, you will get a Form 1099-R where Box 5 will have your Roth 401(k) contributions so you know how much you can withdraw immediately without tax or penalty.
As for your more specific questions:
Conversions/rollovers from Traditional 401(k)? Does it matter if it was rolled over to Traditional IRA then converted vs. converted to Roth 401(k) then rolled over?
I have never heard of anybody doing an in-plan conversion to Roth 401(k), and then rolling over. I am not 100% sure how that would be treated, but I think it would possibly make your entire Roth 401(k) balance earnings (assuming it was zero before). In that case you'd be better off rolling over to an IRA first. Note that as of several years ago you can go straight from a traditional 401(k) to a Roth IRA though; no need to stop in a traditional IRA.
Earnings on converted or rolled over amounts? Presumably earnings on these amounts after the rollover/conversion are treated the same as earnings on regular contributions (is that accurate?), but do the contributions vs. earnings breakdowns in the source account before the rollover/conversion matter?
Yes, earnings after a rollover/conversion are treated the same as any other earnings. For a traditional 401(k) or IRA rollover/conversion, how much is earnings beforehand doesn't matter, because it's the amount rolled over or converted that gets the special withdrawal treatment. But for a Roth 401(k) rollover, the contributions versus earnings do matter, as I detailed above.