Okay, let's tell the story one step at a time:

Closed a Traditional IRA by taking a complete distribution with no taxes withheld (gross distribution) and hands it over to a new Traditional IRA for deposit within the allowed timeframe (typically 60 days, or if considered distributed under covid-CARES, the timeframe was untl Aug). If so, that doesn't count against the "one per 12 months" (the rule is not One Per Year).

If taxes were withheld, the rollover would need to be refilled to Gross using other funds available. Or, the partial amount not refilled is a taxable distribution.

Or, it didn't qualify for rollover. But we are assuming at this point there was a legit rollover.

Then, she did the very same thing, again.

"On the second distribution I can mark as non-rollover and the tax will calculate correctly."

This is why it is step by step. Sure, that takes care of tax treatment, penalty.

"No she didn't put back the RMD by August 31, 2020"

Wait, which part was an RMD? Are you explaining that the "small distribution from 3rd provider" was really RMD?

There seems to be a disallowed rollover. If you can get that back (corrective distribution) before filing the tax form, it's as if it never happened (well, some of it). There likely will be some earnings, which will be subject to penalty.

https://www.irs.gov/retirement-plans/plan-participant-employee/rollovers-of-retirement-plan-and-ira-...

"Tax consequences of the one-rollover-per-year limit

Beginning in 2015, if you receive a distribution from an IRA of previously untaxed amounts:

• you must include the amounts in gross income if you made an IRA-to-IRA rollover in the preceding 12 months (unless the transition rule above applies), and
• you may be subject to the 10% early withdrawal tax on the amounts you include in gross income.

Additionally, if you pay the distributed amounts into another (or the same) IRA, the amounts may be:

• treated as an excess contribution, and
• taxed at 6% per year as long as they remain in the IRA."

https://www.irs.gov/retirement-plans/ira-one-rollover-per-year-rule

And that's why Question 2 doesn't apply. You don't have a Contribution, there is no new money and there is no expectation of Earnings related to rollover activities. It's just moving around the funds, and it's supposed to be within the allowed provisions between the various types (such as, employer pan to traditional IRA doesn't fall in the one-every-12-month limit) and some of the movement is a conversion from sheltered and never-taxed to taxable event or taxable distribution. That's also why you track Basis, so that you don't pay taxes on money you put into retirement already post-tax. So, that's one thing you don't have to worry about.