Q-1: Correct on both parts 1 and 2.
Q-2: Correct on both parts 1 and 2. Because the rollover from the 401(k) means that you will have a nonzero balance in traditional IRAs, your Roth conversion of the recharacterized funds will be partially, perhaps mostly taxable, calculated on your 2023 Form 8606. The relative timing of this Roth conversion and the rollover from the 401(k) to the traditional IRA is irrelevant. Nothing about the rollovers themselves from the 401(k) to the traditional and Roth IRAs goes on Form 8606.
If the rollovers from the 401(k) to the traditional and Roth IRAs came entirely from the traditional account in the 401(k) and were both direct rollovers, you'll receive only one Form 1099-R for the combined amount of the distributions that you will need to split into two for entry into TurboTax because TurboTax only allows for the designation of one type of receiving account for any one 1099-R.
