"3- The IRA Contributions that were never taken as tax deductions and converted to Roth are not taxable?"
That's Basis, and not taxable.
4- Are the IRA earnings that were converted to Roth taxable?"
Yes. And now you have a problem.
If your client has commingled funds, you will want to learn how Pro Rata works. You can't take a specific amount from a Trad IRA to convert and call it Backdoor. There are no ordering rules in conversion.
Backdoor only works as fully nontaxable if all they had in the source account was Basis. Otherwise it's pro rata taxable, every time.
Like this:
For purposes of this process, aggregate Trad IRA, SEP IRA and SIMPLE IRA accounts.
Any contribution that was never deducted is Basis. Other funds in the account(s) would be pre-tax contributions, rollovers from employer plans, and untaxed earnings.
When they "backdoor" that's just a conversion. The backdoor process relies on having only basis and converting from Trad to Roth before there are any earnings, too. Once there are commingled funds, it is pro rata taxable.
Basis amount divided by FMV of aggregated accounts at year end = % Basis. Let's start an example:
$6,000 Basis contributed, $3,000 contribution deducted years ago, account(s) grew to $10,000 FMV.
$6,000 / $10,000. So, 60% is Basis, 40% has never been taxed ($3,000 deductible contributed + $1,000 growth). Let's convert $5,000.
Next, Converted amount * % basis.
$5,000 * 60% = $3,000 is Basis in the conversion (not taxable).
Converted amount minus basis amount = Taxable amount.
$5,000 - $3,000 = $2,000 taxable.
And going back to the account(s) aggregated:
$10,000 FMV minus $5,000 converted = $5,000 in account(s).
$3,000 basis removed from $6,000 basis, so now it is $3,00 basis remaining and the rest is the untaxed. Next conversion, you use the $3,000 Basis + any new basis, of course, for conversion against the new FMV.
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