The deadline for rolling over a distribution from an IRA is the 60th day following the date that the distribution was received, so it's too late to roll over the $14k of distributions made in 2021. For these distributions you can use the education-expense exception to the early distribution penalty, so you'll owe the tax but not the penalty.
For the distributions made in 2022 you must take into account the one-rollover-per-12-months limitation. You can roll one of them over to a traditional IRA, avoiding penalty and continuing to defer the taxes. The others could be rolled over to a Roth IRA as Roth conversions within 60 days of the distribution since Roth conversions are disregarded with respect to the oe-rollover-per-12-months limitation, avoiding the penalty but paying taxes in 2022.
The underpayment penalty is part of your tax liability. The US tax system is pay-as-you-go, so to avoid an underpayment penalty you need to pay estimated taxes or have taxes withheld sufficient to avoid the penalty. Any excess tax paid or balance due is determined on your tax return.
https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes
