- I understand that I'm supposed to remove all earnings attributable to this ineligible contribution--is there a formula for computing this?
That's if you withdraw (aka remove or correct) the excess contributions (by Oct. 15). See pub 590a 'Excess Contributions Withdrawn' for Roth and the more detailed version for trad which links to the same worksheet used for recharacterization. As all three say, normally the trustee or custodian computes this for you, so you don't need to know the formula although you may prefer to check or just understand it.
As the text just above that third links says, for a recharacterization you move both the contribution (principal) and the attributable income (earnings), from the 'wrong' IRA to the 'right' one, but you don't remove or withdraw anything.
- I understand that I am to report the earnings portion of the recharacterization--will my brokerage give me a form that contains this information?
Again for removing an excess contribution you need to report the attributable earnings for the year of the contribution here 2019; yes this should be reported to you (and also to IRS) on form 1099-R. See my recent answer to this somewhat different question (except that since Feb. 10 the 2019 Pub 590A IS available).
For a recharacterization you don't; both the principal and earnings are moved to the 'right' IRA and kept there, just as if the contribution had been there from the start (but invested the way it was in the 'wrong' IRA, which might not have been done or possible in the 'right' one).
- Will the recharacterization to a traditional IRA count as a contribution for 2019 or for 2020? I was hoping to contribute an additional 6,000 for 2020 before doing the conversion back to a Roth.
See previous point; it will count as a contribution for 2019. You can still make a contribution for 2020. If you do so before April 15, be sure to designate which year it is for correctly on the custodian's form(s), so you don't cause additional mistakes and problems. When you do the conversion, the earnings will be reported as taxable (ordinary) income for this year (2020) on the 1099-R in Jan. 2021. If this amount will be enough to affect your 2020 tax significantly (which I wouldn't expect) you still have time to adjust withholding or make estimated payments for 2020 as necessary.
Added: I forgot to note: this only works well if you DON'T already have a trad IRA with significant pretax money (deductible contributions and/or earnings). In that case the conversion part of the backdoor is diluted: you must convert a pro-rata part of the pretax money and pay tax on it now, while a part of the posttax contribution 'basis' remains in the IRA until retirement or future conversion. In other words, recharacterization or removal/correction applies to a specific contribution plus its earnings, but conversion applies to the aggregate total, as does normal (i.e. retirement) distribution. This is true even if you have multiple accounts, even with different custodians: you may give the instructions to -- and get 1099(s) from -- only one or some custodian(s), but on your tax return you have to add all the accounts together.