Tax and penalties applicable when doing Roth IRA -> Traditional IRA -> Roth IRA

Hi, here's a quick timeline of events and the questions I have:

1. In 2022, I contributed $6000 (the max) for my 2022 Roth IRA account and invested the cash into various mutual funds.
2. In 2023, I recharacterized all the 2022 Roth IRA "in kind" into a Traditional IRA due to income limits. As I had $100 of earnings, a total of $6100 ($6000 original contribution + $100 earnings) was put into Traditional IRA.
3. A few days after the recharacterization, I converted the Traditional IRA back to Roth IRA. As I had an additional $50 of earnings, a total of $6150 ($6100 + $50) was put into my Roth IRA account. 
4. All of the above has been done before tax deadline plus extentions 

Based off this sequence of operations, I want to know what tax and penalites I can expect.

1. Will I incur any 10% early distribution penalty given the above has been done before tax deadline plus extentions?
2. My understanding is that any applicable taxes here will be at ordinary income tax rates. How do taxes work on earnings in this senario? Is it the case that taxes will calulated as the delta between the original contribution ($6000) and the value that is taken out after each conversion/recharacterization? E.g. recharacterzation event earnings yeild ($6100 - $6000) = $100  and the conversion event yeild ($6150 - $6000) = $150 so taxes would be ($100 * taxes) + ($150 * taxes). Or would it be the case that the taxes are calculated as the delta between the value I put in and the value that is taken out after each conversion/recharacterization? E.g.  recharacterzation event earnings yeild ($6100 - $6000) = $100 and the conversion event yeild ($6150 - $6100) = $50 so taxes would be ($100 * taxes) + ($50 * taxes). Or is neither the case? 
3. My brokerage says I will get the tax docs related to theese events in Feb 2024 given I executed the above operations in 2023. Would all taxes and penalites be only applicable for tax year 2022 and I need to report as such on my 2022 tax return, meaning I should expect no taxes of penalites related to the above operations for tax year 2023?